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An element “lives” in a space


Should I use hyphens with prefixes like “sub” and “semi”?Why abbreviation for “Definition” as “Def^n” (math context)Do we have to use ordinals with largest/smallest?“Under the condition that” within the realm of probailityThree sentences regarding the definitive article in technical/mathematical writingHow to refer to the variable being added in a weighted sum?hyphen in adjectives with mathematical symbolsIdiomatic way of implying “by a multiplicative factor”Meaning of this (convoluted) sentence from the book “Probably Approximately Correct”How to read (x - y) ^ 2






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








0















I have seen the expression, "X is the Hilbert space in which the element x lives". As a native speaker, this seems quite sloppy to me. Is there a more succinct way to formulate this expression?










share|improve this question

















  • 2





    You're probably venturing into the crossover between the English language and the language of Mathematics. So English language rules don't always apply.

    – KillingTime
    Mar 29 at 15:40











  • What's wrong with that is the house in which the woman lives? Would you rather it be phrased that is the house where the woman lives? If so, then rephrase your sentence the same way: X is the Hilbert space where the element x lives. Or are you objecting on different grounds? If so, what are they?

    – Jason Bassford
    Mar 29 at 16:17












  • @JasonBassford I am dubious as to whether "lives" is an appropriate word in spite of the fact that it's often used colloquially (in a mathematical context). A woman may clearly "live" in a house. My question, I thought, was clearly whether an element may similarly "live" in a space. A vector space is a somewhat different concept to a house. Do we "live" in a/the universe (which I suppose one can consider as being akin to a mathematical space)?

    – Kemal Raik
    Mar 29 at 17:59











  • I certainly think I live in my apartment, in my city, in my country, on this planet, and so on. So, is your objection about not owning the particularly named space—or is it about something without consciousness being able to be described as living anywhere?

    – Jason Bassford
    Mar 29 at 18:08







  • 4





    This is informal, but I have heard almost the exact sentence in many academic talks and graduate level classes, so I'd call it verbally acceptable. I probably wouldn't put it in a paper though.

    – BenL
    Mar 29 at 21:50

















0















I have seen the expression, "X is the Hilbert space in which the element x lives". As a native speaker, this seems quite sloppy to me. Is there a more succinct way to formulate this expression?










share|improve this question

















  • 2





    You're probably venturing into the crossover between the English language and the language of Mathematics. So English language rules don't always apply.

    – KillingTime
    Mar 29 at 15:40











  • What's wrong with that is the house in which the woman lives? Would you rather it be phrased that is the house where the woman lives? If so, then rephrase your sentence the same way: X is the Hilbert space where the element x lives. Or are you objecting on different grounds? If so, what are they?

    – Jason Bassford
    Mar 29 at 16:17












  • @JasonBassford I am dubious as to whether "lives" is an appropriate word in spite of the fact that it's often used colloquially (in a mathematical context). A woman may clearly "live" in a house. My question, I thought, was clearly whether an element may similarly "live" in a space. A vector space is a somewhat different concept to a house. Do we "live" in a/the universe (which I suppose one can consider as being akin to a mathematical space)?

    – Kemal Raik
    Mar 29 at 17:59











  • I certainly think I live in my apartment, in my city, in my country, on this planet, and so on. So, is your objection about not owning the particularly named space—or is it about something without consciousness being able to be described as living anywhere?

    – Jason Bassford
    Mar 29 at 18:08







  • 4





    This is informal, but I have heard almost the exact sentence in many academic talks and graduate level classes, so I'd call it verbally acceptable. I probably wouldn't put it in a paper though.

    – BenL
    Mar 29 at 21:50













0












0








0








I have seen the expression, "X is the Hilbert space in which the element x lives". As a native speaker, this seems quite sloppy to me. Is there a more succinct way to formulate this expression?










share|improve this question














I have seen the expression, "X is the Hilbert space in which the element x lives". As a native speaker, this seems quite sloppy to me. Is there a more succinct way to formulate this expression?







mathematics






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Mar 29 at 15:22









Kemal RaikKemal Raik

11




11







  • 2





    You're probably venturing into the crossover between the English language and the language of Mathematics. So English language rules don't always apply.

    – KillingTime
    Mar 29 at 15:40











  • What's wrong with that is the house in which the woman lives? Would you rather it be phrased that is the house where the woman lives? If so, then rephrase your sentence the same way: X is the Hilbert space where the element x lives. Or are you objecting on different grounds? If so, what are they?

    – Jason Bassford
    Mar 29 at 16:17












  • @JasonBassford I am dubious as to whether "lives" is an appropriate word in spite of the fact that it's often used colloquially (in a mathematical context). A woman may clearly "live" in a house. My question, I thought, was clearly whether an element may similarly "live" in a space. A vector space is a somewhat different concept to a house. Do we "live" in a/the universe (which I suppose one can consider as being akin to a mathematical space)?

    – Kemal Raik
    Mar 29 at 17:59











  • I certainly think I live in my apartment, in my city, in my country, on this planet, and so on. So, is your objection about not owning the particularly named space—or is it about something without consciousness being able to be described as living anywhere?

    – Jason Bassford
    Mar 29 at 18:08







  • 4





    This is informal, but I have heard almost the exact sentence in many academic talks and graduate level classes, so I'd call it verbally acceptable. I probably wouldn't put it in a paper though.

    – BenL
    Mar 29 at 21:50












  • 2





    You're probably venturing into the crossover between the English language and the language of Mathematics. So English language rules don't always apply.

    – KillingTime
    Mar 29 at 15:40











  • What's wrong with that is the house in which the woman lives? Would you rather it be phrased that is the house where the woman lives? If so, then rephrase your sentence the same way: X is the Hilbert space where the element x lives. Or are you objecting on different grounds? If so, what are they?

    – Jason Bassford
    Mar 29 at 16:17












  • @JasonBassford I am dubious as to whether "lives" is an appropriate word in spite of the fact that it's often used colloquially (in a mathematical context). A woman may clearly "live" in a house. My question, I thought, was clearly whether an element may similarly "live" in a space. A vector space is a somewhat different concept to a house. Do we "live" in a/the universe (which I suppose one can consider as being akin to a mathematical space)?

    – Kemal Raik
    Mar 29 at 17:59











  • I certainly think I live in my apartment, in my city, in my country, on this planet, and so on. So, is your objection about not owning the particularly named space—or is it about something without consciousness being able to be described as living anywhere?

    – Jason Bassford
    Mar 29 at 18:08







  • 4





    This is informal, but I have heard almost the exact sentence in many academic talks and graduate level classes, so I'd call it verbally acceptable. I probably wouldn't put it in a paper though.

    – BenL
    Mar 29 at 21:50







2




2





You're probably venturing into the crossover between the English language and the language of Mathematics. So English language rules don't always apply.

– KillingTime
Mar 29 at 15:40





You're probably venturing into the crossover between the English language and the language of Mathematics. So English language rules don't always apply.

– KillingTime
Mar 29 at 15:40













What's wrong with that is the house in which the woman lives? Would you rather it be phrased that is the house where the woman lives? If so, then rephrase your sentence the same way: X is the Hilbert space where the element x lives. Or are you objecting on different grounds? If so, what are they?

– Jason Bassford
Mar 29 at 16:17






What's wrong with that is the house in which the woman lives? Would you rather it be phrased that is the house where the woman lives? If so, then rephrase your sentence the same way: X is the Hilbert space where the element x lives. Or are you objecting on different grounds? If so, what are they?

– Jason Bassford
Mar 29 at 16:17














@JasonBassford I am dubious as to whether "lives" is an appropriate word in spite of the fact that it's often used colloquially (in a mathematical context). A woman may clearly "live" in a house. My question, I thought, was clearly whether an element may similarly "live" in a space. A vector space is a somewhat different concept to a house. Do we "live" in a/the universe (which I suppose one can consider as being akin to a mathematical space)?

– Kemal Raik
Mar 29 at 17:59





@JasonBassford I am dubious as to whether "lives" is an appropriate word in spite of the fact that it's often used colloquially (in a mathematical context). A woman may clearly "live" in a house. My question, I thought, was clearly whether an element may similarly "live" in a space. A vector space is a somewhat different concept to a house. Do we "live" in a/the universe (which I suppose one can consider as being akin to a mathematical space)?

– Kemal Raik
Mar 29 at 17:59













I certainly think I live in my apartment, in my city, in my country, on this planet, and so on. So, is your objection about not owning the particularly named space—or is it about something without consciousness being able to be described as living anywhere?

– Jason Bassford
Mar 29 at 18:08






I certainly think I live in my apartment, in my city, in my country, on this planet, and so on. So, is your objection about not owning the particularly named space—or is it about something without consciousness being able to be described as living anywhere?

– Jason Bassford
Mar 29 at 18:08





4




4





This is informal, but I have heard almost the exact sentence in many academic talks and graduate level classes, so I'd call it verbally acceptable. I probably wouldn't put it in a paper though.

– BenL
Mar 29 at 21:50





This is informal, but I have heard almost the exact sentence in many academic talks and graduate level classes, so I'd call it verbally acceptable. I probably wouldn't put it in a paper though.

– BenL
Mar 29 at 21:50










4 Answers
4






active

oldest

votes


















0














You could say:




X is in the Hilbert space to which the element x belongs.




Though I don't think using "lives" is necessarily wrong (it is a bit informal, though).






share|improve this answer























  • I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

    – Kemal Raik
    Mar 29 at 15:28






  • 1





    @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

    – satnam
    Mar 29 at 20:35











  • Belongs has the connotation that it might be found outside of it and would need to be put back in.

    – Jim
    Mar 30 at 4:34











  • @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

    – AleksandrH
    Mar 30 at 12:30











  • @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

    – Jim
    Mar 30 at 15:10


















0














This usage of lives is an anthropomorphisation: human attributes and behaviours are affixed to an abstract object in order to make it more accessible to the usual human thought patterns.



If you want to, you can substitute occurs:




X is the Hilbert space in which element x occurs.




or, since lives implies it cannot "live" elsewhere (which is why anthropomorphizations are such a powerful tool)




Element x only occurs in Hilbert space X.







share|improve this answer























  • This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

    – BenL
    Mar 29 at 22:14











  • I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

    – Hot Licks
    Mar 29 at 23:47












  • Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

    – Hot Licks
    Mar 29 at 23:49



















0














You ask about succinctness, but then you put quotes around "lives," so it's not clear what exactly you're asking.



Where



To make it more succinct, the word "where" can be substituted for "in which." That would make it more succinct. While using "where" to mean "in which" for the abstract is widely considered to be informal and is something one would avoid in an academic paper, like a thesis or dissertation, that isn't the case here. That's because the sentence use the word "space," making the meaning literal rather than abstract.



Lives



Regarding "lives," that's about as succinct as succinct gets.



I'm wondering if you're suggesting that another verb might be more apt, like maybe because the word "element" refers to something that is inanimate. I can't be sure that's what you mean, though, because "element" can refer to living things, too, like when we say, "An unsavory element has moved in down the street and has taken up living in Mr. and Mrs. Smith's old house." Without more context, for the singular contextual clue of "Hilbert" means nothing to me, I can't be sure what you're driving at.



What I can say about using "lives" there, though, is I don't have a problem with using the verb "lives" for the subject "element" even if "element" refers to something inanimate. Such a usage would merely employ imagery, an imagery that paints a very vivid picture that could be quite apropos to the circumstances, even most succinct.



While you could certainly switch "lives" out for another verb like "exists" or "occurs," doing so would come across quite differently to readers because using the verb "lives" for the subject "element," if inanimate, personifies or anthropomorphizes "element" such that it imbues it with a certain unrelenting permanence, like as if it willed itself there, or imbues it with a certain unpredictable, ongoing effect on the environs, like as if it behaved with freewill.



Therefore, because of the substantive difference in how "lives" comes across and because I operate from a position that people say what they mean and mean what they say unless I'm on solid ground to know otherwise, I would be extremely reluctant if I were you to say that "lives" is wrong or to criticize another writer as being "sloppy" or less "succinct" for using "lives" there.






share|improve this answer
































    0














    I don't see a problem with "lives", said of imaginary inhabitants of various dimensional spaces. Many mathematicians and scientists have read Abbot's Flatland, I imagine, and found it an aid to the intuition to think of what it would be like to live in a space with a different dimensionality.






    share|improve this answer























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      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      0














      You could say:




      X is in the Hilbert space to which the element x belongs.




      Though I don't think using "lives" is necessarily wrong (it is a bit informal, though).






      share|improve this answer























      • I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

        – Kemal Raik
        Mar 29 at 15:28






      • 1





        @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

        – satnam
        Mar 29 at 20:35











      • Belongs has the connotation that it might be found outside of it and would need to be put back in.

        – Jim
        Mar 30 at 4:34











      • @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

        – AleksandrH
        Mar 30 at 12:30











      • @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

        – Jim
        Mar 30 at 15:10















      0














      You could say:




      X is in the Hilbert space to which the element x belongs.




      Though I don't think using "lives" is necessarily wrong (it is a bit informal, though).






      share|improve this answer























      • I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

        – Kemal Raik
        Mar 29 at 15:28






      • 1





        @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

        – satnam
        Mar 29 at 20:35











      • Belongs has the connotation that it might be found outside of it and would need to be put back in.

        – Jim
        Mar 30 at 4:34











      • @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

        – AleksandrH
        Mar 30 at 12:30











      • @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

        – Jim
        Mar 30 at 15:10













      0












      0








      0







      You could say:




      X is in the Hilbert space to which the element x belongs.




      Though I don't think using "lives" is necessarily wrong (it is a bit informal, though).






      share|improve this answer













      You could say:




      X is in the Hilbert space to which the element x belongs.




      Though I don't think using "lives" is necessarily wrong (it is a bit informal, though).







      share|improve this answer












      share|improve this answer



      share|improve this answer










      answered Mar 29 at 15:24









      AleksandrHAleksandrH

      2,139926




      2,139926












      • I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

        – Kemal Raik
        Mar 29 at 15:28






      • 1





        @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

        – satnam
        Mar 29 at 20:35











      • Belongs has the connotation that it might be found outside of it and would need to be put back in.

        – Jim
        Mar 30 at 4:34











      • @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

        – AleksandrH
        Mar 30 at 12:30











      • @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

        – Jim
        Mar 30 at 15:10

















      • I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

        – Kemal Raik
        Mar 29 at 15:28






      • 1





        @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

        – satnam
        Mar 29 at 20:35











      • Belongs has the connotation that it might be found outside of it and would need to be put back in.

        – Jim
        Mar 30 at 4:34











      • @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

        – AleksandrH
        Mar 30 at 12:30











      • @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

        – Jim
        Mar 30 at 15:10
















      I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

      – Kemal Raik
      Mar 29 at 15:28





      I agree that "lives" does not seem to be necessarily incorrect, but indeed, a tad informal. Additionally, I'd like to ask: do you think it's better to write "X is the Hilbert space in which the element x belongs" or your version? I suppose it depends on whether it's better to say an element "belongs to" or "belongs in" a space. In retrospect, I suppose your version seems more correct.

      – Kemal Raik
      Mar 29 at 15:28




      1




      1





      @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

      – satnam
      Mar 29 at 20:35





      @KemalRaik read this: ell.stackexchange.com/questions/32375/…. Summary: Use belongs to.

      – satnam
      Mar 29 at 20:35













      Belongs has the connotation that it might be found outside of it and would need to be put back in.

      – Jim
      Mar 30 at 4:34





      Belongs has the connotation that it might be found outside of it and would need to be put back in.

      – Jim
      Mar 30 at 4:34













      @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

      – AleksandrH
      Mar 30 at 12:30





      @Jim It largely depends on the context. A Hilbert space is a mathematical notion. Based my coursework, I believe "belongs" is an accurate term.

      – AleksandrH
      Mar 30 at 12:30













      @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

      – Jim
      Mar 30 at 15:10





      @AleksandrH I was really responding to the ‘belongs in’ question, but I didn’t make it very clear. I like ‘belongs to’ as well. But not ‘belongs in’- which has the connotation I mention.

      – Jim
      Mar 30 at 15:10













      0














      This usage of lives is an anthropomorphisation: human attributes and behaviours are affixed to an abstract object in order to make it more accessible to the usual human thought patterns.



      If you want to, you can substitute occurs:




      X is the Hilbert space in which element x occurs.




      or, since lives implies it cannot "live" elsewhere (which is why anthropomorphizations are such a powerful tool)




      Element x only occurs in Hilbert space X.







      share|improve this answer























      • This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

        – BenL
        Mar 29 at 22:14











      • I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

        – Hot Licks
        Mar 29 at 23:47












      • Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

        – Hot Licks
        Mar 29 at 23:49
















      0














      This usage of lives is an anthropomorphisation: human attributes and behaviours are affixed to an abstract object in order to make it more accessible to the usual human thought patterns.



      If you want to, you can substitute occurs:




      X is the Hilbert space in which element x occurs.




      or, since lives implies it cannot "live" elsewhere (which is why anthropomorphizations are such a powerful tool)




      Element x only occurs in Hilbert space X.







      share|improve this answer























      • This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

        – BenL
        Mar 29 at 22:14











      • I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

        – Hot Licks
        Mar 29 at 23:47












      • Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

        – Hot Licks
        Mar 29 at 23:49














      0












      0








      0







      This usage of lives is an anthropomorphisation: human attributes and behaviours are affixed to an abstract object in order to make it more accessible to the usual human thought patterns.



      If you want to, you can substitute occurs:




      X is the Hilbert space in which element x occurs.




      or, since lives implies it cannot "live" elsewhere (which is why anthropomorphizations are such a powerful tool)




      Element x only occurs in Hilbert space X.







      share|improve this answer













      This usage of lives is an anthropomorphisation: human attributes and behaviours are affixed to an abstract object in order to make it more accessible to the usual human thought patterns.



      If you want to, you can substitute occurs:




      X is the Hilbert space in which element x occurs.




      or, since lives implies it cannot "live" elsewhere (which is why anthropomorphizations are such a powerful tool)




      Element x only occurs in Hilbert space X.








      share|improve this answer












      share|improve this answer



      share|improve this answer










      answered Mar 29 at 20:23









      BassBass

      20713




      20713












      • This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

        – BenL
        Mar 29 at 22:14











      • I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

        – Hot Licks
        Mar 29 at 23:47












      • Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

        – Hot Licks
        Mar 29 at 23:49


















      • This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

        – BenL
        Mar 29 at 22:14











      • I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

        – Hot Licks
        Mar 29 at 23:47












      • Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

        – Hot Licks
        Mar 29 at 23:49

















      This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

      – BenL
      Mar 29 at 22:14





      This is far beyond the ESE, but can anything be expressed in only a single Hilbert space? If not, then perhaps "lives" is just wrong instead of informal. Perhaps "X is a Hilbert space in which element x can be expressed" would then be more accurate.

      – BenL
      Mar 29 at 22:14













      I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

      – Hot Licks
      Mar 29 at 23:47






      I would use "exists" rather than "occurs". "Occurs" gives the impression that it pops into existence somehow (which may be true, but is a whole 'nother chapter in physics).

      – Hot Licks
      Mar 29 at 23:47














      Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

      – Hot Licks
      Mar 29 at 23:49






      Another option is "resides". And maybe some synonyms of that: dwells, occupies, abides, et al.

      – Hot Licks
      Mar 29 at 23:49












      0














      You ask about succinctness, but then you put quotes around "lives," so it's not clear what exactly you're asking.



      Where



      To make it more succinct, the word "where" can be substituted for "in which." That would make it more succinct. While using "where" to mean "in which" for the abstract is widely considered to be informal and is something one would avoid in an academic paper, like a thesis or dissertation, that isn't the case here. That's because the sentence use the word "space," making the meaning literal rather than abstract.



      Lives



      Regarding "lives," that's about as succinct as succinct gets.



      I'm wondering if you're suggesting that another verb might be more apt, like maybe because the word "element" refers to something that is inanimate. I can't be sure that's what you mean, though, because "element" can refer to living things, too, like when we say, "An unsavory element has moved in down the street and has taken up living in Mr. and Mrs. Smith's old house." Without more context, for the singular contextual clue of "Hilbert" means nothing to me, I can't be sure what you're driving at.



      What I can say about using "lives" there, though, is I don't have a problem with using the verb "lives" for the subject "element" even if "element" refers to something inanimate. Such a usage would merely employ imagery, an imagery that paints a very vivid picture that could be quite apropos to the circumstances, even most succinct.



      While you could certainly switch "lives" out for another verb like "exists" or "occurs," doing so would come across quite differently to readers because using the verb "lives" for the subject "element," if inanimate, personifies or anthropomorphizes "element" such that it imbues it with a certain unrelenting permanence, like as if it willed itself there, or imbues it with a certain unpredictable, ongoing effect on the environs, like as if it behaved with freewill.



      Therefore, because of the substantive difference in how "lives" comes across and because I operate from a position that people say what they mean and mean what they say unless I'm on solid ground to know otherwise, I would be extremely reluctant if I were you to say that "lives" is wrong or to criticize another writer as being "sloppy" or less "succinct" for using "lives" there.






      share|improve this answer





























        0














        You ask about succinctness, but then you put quotes around "lives," so it's not clear what exactly you're asking.



        Where



        To make it more succinct, the word "where" can be substituted for "in which." That would make it more succinct. While using "where" to mean "in which" for the abstract is widely considered to be informal and is something one would avoid in an academic paper, like a thesis or dissertation, that isn't the case here. That's because the sentence use the word "space," making the meaning literal rather than abstract.



        Lives



        Regarding "lives," that's about as succinct as succinct gets.



        I'm wondering if you're suggesting that another verb might be more apt, like maybe because the word "element" refers to something that is inanimate. I can't be sure that's what you mean, though, because "element" can refer to living things, too, like when we say, "An unsavory element has moved in down the street and has taken up living in Mr. and Mrs. Smith's old house." Without more context, for the singular contextual clue of "Hilbert" means nothing to me, I can't be sure what you're driving at.



        What I can say about using "lives" there, though, is I don't have a problem with using the verb "lives" for the subject "element" even if "element" refers to something inanimate. Such a usage would merely employ imagery, an imagery that paints a very vivid picture that could be quite apropos to the circumstances, even most succinct.



        While you could certainly switch "lives" out for another verb like "exists" or "occurs," doing so would come across quite differently to readers because using the verb "lives" for the subject "element," if inanimate, personifies or anthropomorphizes "element" such that it imbues it with a certain unrelenting permanence, like as if it willed itself there, or imbues it with a certain unpredictable, ongoing effect on the environs, like as if it behaved with freewill.



        Therefore, because of the substantive difference in how "lives" comes across and because I operate from a position that people say what they mean and mean what they say unless I'm on solid ground to know otherwise, I would be extremely reluctant if I were you to say that "lives" is wrong or to criticize another writer as being "sloppy" or less "succinct" for using "lives" there.






        share|improve this answer



























          0












          0








          0







          You ask about succinctness, but then you put quotes around "lives," so it's not clear what exactly you're asking.



          Where



          To make it more succinct, the word "where" can be substituted for "in which." That would make it more succinct. While using "where" to mean "in which" for the abstract is widely considered to be informal and is something one would avoid in an academic paper, like a thesis or dissertation, that isn't the case here. That's because the sentence use the word "space," making the meaning literal rather than abstract.



          Lives



          Regarding "lives," that's about as succinct as succinct gets.



          I'm wondering if you're suggesting that another verb might be more apt, like maybe because the word "element" refers to something that is inanimate. I can't be sure that's what you mean, though, because "element" can refer to living things, too, like when we say, "An unsavory element has moved in down the street and has taken up living in Mr. and Mrs. Smith's old house." Without more context, for the singular contextual clue of "Hilbert" means nothing to me, I can't be sure what you're driving at.



          What I can say about using "lives" there, though, is I don't have a problem with using the verb "lives" for the subject "element" even if "element" refers to something inanimate. Such a usage would merely employ imagery, an imagery that paints a very vivid picture that could be quite apropos to the circumstances, even most succinct.



          While you could certainly switch "lives" out for another verb like "exists" or "occurs," doing so would come across quite differently to readers because using the verb "lives" for the subject "element," if inanimate, personifies or anthropomorphizes "element" such that it imbues it with a certain unrelenting permanence, like as if it willed itself there, or imbues it with a certain unpredictable, ongoing effect on the environs, like as if it behaved with freewill.



          Therefore, because of the substantive difference in how "lives" comes across and because I operate from a position that people say what they mean and mean what they say unless I'm on solid ground to know otherwise, I would be extremely reluctant if I were you to say that "lives" is wrong or to criticize another writer as being "sloppy" or less "succinct" for using "lives" there.






          share|improve this answer















          You ask about succinctness, but then you put quotes around "lives," so it's not clear what exactly you're asking.



          Where



          To make it more succinct, the word "where" can be substituted for "in which." That would make it more succinct. While using "where" to mean "in which" for the abstract is widely considered to be informal and is something one would avoid in an academic paper, like a thesis or dissertation, that isn't the case here. That's because the sentence use the word "space," making the meaning literal rather than abstract.



          Lives



          Regarding "lives," that's about as succinct as succinct gets.



          I'm wondering if you're suggesting that another verb might be more apt, like maybe because the word "element" refers to something that is inanimate. I can't be sure that's what you mean, though, because "element" can refer to living things, too, like when we say, "An unsavory element has moved in down the street and has taken up living in Mr. and Mrs. Smith's old house." Without more context, for the singular contextual clue of "Hilbert" means nothing to me, I can't be sure what you're driving at.



          What I can say about using "lives" there, though, is I don't have a problem with using the verb "lives" for the subject "element" even if "element" refers to something inanimate. Such a usage would merely employ imagery, an imagery that paints a very vivid picture that could be quite apropos to the circumstances, even most succinct.



          While you could certainly switch "lives" out for another verb like "exists" or "occurs," doing so would come across quite differently to readers because using the verb "lives" for the subject "element," if inanimate, personifies or anthropomorphizes "element" such that it imbues it with a certain unrelenting permanence, like as if it willed itself there, or imbues it with a certain unpredictable, ongoing effect on the environs, like as if it behaved with freewill.



          Therefore, because of the substantive difference in how "lives" comes across and because I operate from a position that people say what they mean and mean what they say unless I'm on solid ground to know otherwise, I would be extremely reluctant if I were you to say that "lives" is wrong or to criticize another writer as being "sloppy" or less "succinct" for using "lives" there.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Mar 30 at 0:45

























          answered Mar 29 at 23:43









          Benjamin HarmanBenjamin Harman

          5,74031740




          5,74031740





















              0














              I don't see a problem with "lives", said of imaginary inhabitants of various dimensional spaces. Many mathematicians and scientists have read Abbot's Flatland, I imagine, and found it an aid to the intuition to think of what it would be like to live in a space with a different dimensionality.






              share|improve this answer



























                0














                I don't see a problem with "lives", said of imaginary inhabitants of various dimensional spaces. Many mathematicians and scientists have read Abbot's Flatland, I imagine, and found it an aid to the intuition to think of what it would be like to live in a space with a different dimensionality.






                share|improve this answer

























                  0












                  0








                  0







                  I don't see a problem with "lives", said of imaginary inhabitants of various dimensional spaces. Many mathematicians and scientists have read Abbot's Flatland, I imagine, and found it an aid to the intuition to think of what it would be like to live in a space with a different dimensionality.






                  share|improve this answer













                  I don't see a problem with "lives", said of imaginary inhabitants of various dimensional spaces. Many mathematicians and scientists have read Abbot's Flatland, I imagine, and found it an aid to the intuition to think of what it would be like to live in a space with a different dimensionality.







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered Mar 30 at 1:27









                  Greg LeeGreg Lee

                  15k2933




                  15k2933



























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