Variables and Mathematical Language [on hold]
I'm trying to make sense of some of the language we employ when using variables in mathematics. The textbook definition of a variable as "a symbol that temporarily stands for a known or unknown object" doesn't seem to account for all the uses of variables.
1.) Defining Statements.
In math, we might say "Let x be the number 2." It seems to me that this is an incorrect use of the state of being verb "be." We would typically use "be" to assert that two things are the same. However, in the variable defining statement, "x" has not yet been defined, so it makes no sense to say "x is 2." Instead, I feel the sentence should be "Let x stand for the number 2" or "Let the value of x be 2." Both of these sentences are unambiguous because 'x' refers unambiguously to the symbol 'x' and we are letting the symbol 'x' represent the mathematical object 2.
There are many other kinds of defining statements where one runs into this kind of trouble. We say things like "Let x = 2", "Set x = 2", "Choose x = 2", etc. Compare these with the english sentence "Let him be a merchant." In the english sentence, "him" presumably refers to a fixed individual (though we don't necessarily know who without context) whereas the 'x' in the above three sentences refers to nothing before the = sign (functioning as the verb 'equals').
2.) If/then Statements.
We discussing even numbers, we might say something like "If x is even, then x is divisible by 2," or "x is divisible by 2 when x is even." If 'x' refers to a fixed (though possibly unknown) object, then why does it make sense to ask if or when x has some property?
3.) Quantified Statements.
In algebra we might make a statement like "x+1 = 1+x for all x." Once again if 'x' refers to a fixed object, then speaking about 'all x' doesn't make sense.
We also say things like "x+1=2 for some x." If 'x' is a name, why does it make sense to talk about 'some x'?
4.) Functional Relationships.
Consider the statement "As x gets larger and larger, so does 2x." Mathematical objects do not change with time; e.g. the number 1 is 1, has always been 1, and will never cease to be 1. Thus if 'x' is the name of some object, such as the number 1, it makes no sense to speak of 'x' as getting larger and larger.
It would be great if someone could explain some or all of these usages.
meaning word-usage pronouns mathematics be
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
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put on hold as off-topic by FumbleFingers, TaliesinMerlin, TrevorD, Jason Bassford, JJJ 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "Please include the research you’ve done, or consider if your question suits our English Language Learners site better. Questions that can be answered using commonly-available references are off-topic." – FumbleFingers, TaliesinMerlin, TrevorD, JJJ
If this question can be reworded to fit the rules in the help center, please edit the question.
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I'm trying to make sense of some of the language we employ when using variables in mathematics. The textbook definition of a variable as "a symbol that temporarily stands for a known or unknown object" doesn't seem to account for all the uses of variables.
1.) Defining Statements.
In math, we might say "Let x be the number 2." It seems to me that this is an incorrect use of the state of being verb "be." We would typically use "be" to assert that two things are the same. However, in the variable defining statement, "x" has not yet been defined, so it makes no sense to say "x is 2." Instead, I feel the sentence should be "Let x stand for the number 2" or "Let the value of x be 2." Both of these sentences are unambiguous because 'x' refers unambiguously to the symbol 'x' and we are letting the symbol 'x' represent the mathematical object 2.
There are many other kinds of defining statements where one runs into this kind of trouble. We say things like "Let x = 2", "Set x = 2", "Choose x = 2", etc. Compare these with the english sentence "Let him be a merchant." In the english sentence, "him" presumably refers to a fixed individual (though we don't necessarily know who without context) whereas the 'x' in the above three sentences refers to nothing before the = sign (functioning as the verb 'equals').
2.) If/then Statements.
We discussing even numbers, we might say something like "If x is even, then x is divisible by 2," or "x is divisible by 2 when x is even." If 'x' refers to a fixed (though possibly unknown) object, then why does it make sense to ask if or when x has some property?
3.) Quantified Statements.
In algebra we might make a statement like "x+1 = 1+x for all x." Once again if 'x' refers to a fixed object, then speaking about 'all x' doesn't make sense.
We also say things like "x+1=2 for some x." If 'x' is a name, why does it make sense to talk about 'some x'?
4.) Functional Relationships.
Consider the statement "As x gets larger and larger, so does 2x." Mathematical objects do not change with time; e.g. the number 1 is 1, has always been 1, and will never cease to be 1. Thus if 'x' is the name of some object, such as the number 1, it makes no sense to speak of 'x' as getting larger and larger.
It would be great if someone could explain some or all of these usages.
meaning word-usage pronouns mathematics be
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by FumbleFingers, TaliesinMerlin, TrevorD, Jason Bassford, JJJ 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "Please include the research you’ve done, or consider if your question suits our English Language Learners site better. Questions that can be answered using commonly-available references are off-topic." – FumbleFingers, TaliesinMerlin, TrevorD, JJJ
If this question can be reworded to fit the rules in the help center, please edit the question.
When one says a variable varies, what is meant is that the value is not known in general, but that it can assume many values. When one of these values is assumed (as in Let x be the number 2.), then that is the value of x until further notice, when it might assume another value or be undefined again.
– John Lawler
yesterday
I don't understand why you are assuming that "x" has to refer to a fixed quantity. A variable is literally a quantity that varies or is assumed to vary because the value is unknown. So 1 is 1, but x may change due to a function or other situation, and x may refer to a range of values (for all x in the set of integers...) So are you asking about how English usage within mathematics treats the variable, or how the variable is defined?
– TaliesinMerlin
yesterday
@TaliesinMerlin I am uneasy with the notion of a 'variable quantity' in mathematics because it would be hard, if not impossible, to give a rigorous definition of such a thing. I am trying to interpret the occurrence of x in a sentence as a name for a definitive object, much like how the pronoun 'it' can function as a proper noun in context.
– Visiting_Mathematician
23 hours ago
@Visiting_Mathematician If your unease is about the semantics of a variable, I'd suggest bringing this up in the Mathematics Stack Exchange. English doesn't require rigorous referentiality for expressions to work, as nouns do not necessarily refer to "definitive object[s]" but rather can be signifiers for abstract concepts.
– TaliesinMerlin
22 hours ago
@Visiting_Mathematician A variable is a label that is assigned to a property which can take many values. If a letter takes only one value it's not a variable, it's a constant. A good example of a variable is velocity, often given the label "v". If v is defined as the velocity of a ball thrown vertically upward its value starts off high, decreases to zero then increases as the ball falls back. There is no number which expresses all those instantaneous velocities but they are all valid values of v.
– BoldBen
20 hours ago
|
show 1 more comment
I'm trying to make sense of some of the language we employ when using variables in mathematics. The textbook definition of a variable as "a symbol that temporarily stands for a known or unknown object" doesn't seem to account for all the uses of variables.
1.) Defining Statements.
In math, we might say "Let x be the number 2." It seems to me that this is an incorrect use of the state of being verb "be." We would typically use "be" to assert that two things are the same. However, in the variable defining statement, "x" has not yet been defined, so it makes no sense to say "x is 2." Instead, I feel the sentence should be "Let x stand for the number 2" or "Let the value of x be 2." Both of these sentences are unambiguous because 'x' refers unambiguously to the symbol 'x' and we are letting the symbol 'x' represent the mathematical object 2.
There are many other kinds of defining statements where one runs into this kind of trouble. We say things like "Let x = 2", "Set x = 2", "Choose x = 2", etc. Compare these with the english sentence "Let him be a merchant." In the english sentence, "him" presumably refers to a fixed individual (though we don't necessarily know who without context) whereas the 'x' in the above three sentences refers to nothing before the = sign (functioning as the verb 'equals').
2.) If/then Statements.
We discussing even numbers, we might say something like "If x is even, then x is divisible by 2," or "x is divisible by 2 when x is even." If 'x' refers to a fixed (though possibly unknown) object, then why does it make sense to ask if or when x has some property?
3.) Quantified Statements.
In algebra we might make a statement like "x+1 = 1+x for all x." Once again if 'x' refers to a fixed object, then speaking about 'all x' doesn't make sense.
We also say things like "x+1=2 for some x." If 'x' is a name, why does it make sense to talk about 'some x'?
4.) Functional Relationships.
Consider the statement "As x gets larger and larger, so does 2x." Mathematical objects do not change with time; e.g. the number 1 is 1, has always been 1, and will never cease to be 1. Thus if 'x' is the name of some object, such as the number 1, it makes no sense to speak of 'x' as getting larger and larger.
It would be great if someone could explain some or all of these usages.
meaning word-usage pronouns mathematics be
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm trying to make sense of some of the language we employ when using variables in mathematics. The textbook definition of a variable as "a symbol that temporarily stands for a known or unknown object" doesn't seem to account for all the uses of variables.
1.) Defining Statements.
In math, we might say "Let x be the number 2." It seems to me that this is an incorrect use of the state of being verb "be." We would typically use "be" to assert that two things are the same. However, in the variable defining statement, "x" has not yet been defined, so it makes no sense to say "x is 2." Instead, I feel the sentence should be "Let x stand for the number 2" or "Let the value of x be 2." Both of these sentences are unambiguous because 'x' refers unambiguously to the symbol 'x' and we are letting the symbol 'x' represent the mathematical object 2.
There are many other kinds of defining statements where one runs into this kind of trouble. We say things like "Let x = 2", "Set x = 2", "Choose x = 2", etc. Compare these with the english sentence "Let him be a merchant." In the english sentence, "him" presumably refers to a fixed individual (though we don't necessarily know who without context) whereas the 'x' in the above three sentences refers to nothing before the = sign (functioning as the verb 'equals').
2.) If/then Statements.
We discussing even numbers, we might say something like "If x is even, then x is divisible by 2," or "x is divisible by 2 when x is even." If 'x' refers to a fixed (though possibly unknown) object, then why does it make sense to ask if or when x has some property?
3.) Quantified Statements.
In algebra we might make a statement like "x+1 = 1+x for all x." Once again if 'x' refers to a fixed object, then speaking about 'all x' doesn't make sense.
We also say things like "x+1=2 for some x." If 'x' is a name, why does it make sense to talk about 'some x'?
4.) Functional Relationships.
Consider the statement "As x gets larger and larger, so does 2x." Mathematical objects do not change with time; e.g. the number 1 is 1, has always been 1, and will never cease to be 1. Thus if 'x' is the name of some object, such as the number 1, it makes no sense to speak of 'x' as getting larger and larger.
It would be great if someone could explain some or all of these usages.
meaning word-usage pronouns mathematics be
meaning word-usage pronouns mathematics be
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
asked yesterday
Visiting_MathematicianVisiting_Mathematician
21
21
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Visiting_Mathematician is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by FumbleFingers, TaliesinMerlin, TrevorD, Jason Bassford, JJJ 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "Please include the research you’ve done, or consider if your question suits our English Language Learners site better. Questions that can be answered using commonly-available references are off-topic." – FumbleFingers, TaliesinMerlin, TrevorD, JJJ
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by FumbleFingers, TaliesinMerlin, TrevorD, Jason Bassford, JJJ 5 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "Please include the research you’ve done, or consider if your question suits our English Language Learners site better. Questions that can be answered using commonly-available references are off-topic." – FumbleFingers, TaliesinMerlin, TrevorD, JJJ
If this question can be reworded to fit the rules in the help center, please edit the question.
When one says a variable varies, what is meant is that the value is not known in general, but that it can assume many values. When one of these values is assumed (as in Let x be the number 2.), then that is the value of x until further notice, when it might assume another value or be undefined again.
– John Lawler
yesterday
I don't understand why you are assuming that "x" has to refer to a fixed quantity. A variable is literally a quantity that varies or is assumed to vary because the value is unknown. So 1 is 1, but x may change due to a function or other situation, and x may refer to a range of values (for all x in the set of integers...) So are you asking about how English usage within mathematics treats the variable, or how the variable is defined?
– TaliesinMerlin
yesterday
@TaliesinMerlin I am uneasy with the notion of a 'variable quantity' in mathematics because it would be hard, if not impossible, to give a rigorous definition of such a thing. I am trying to interpret the occurrence of x in a sentence as a name for a definitive object, much like how the pronoun 'it' can function as a proper noun in context.
– Visiting_Mathematician
23 hours ago
@Visiting_Mathematician If your unease is about the semantics of a variable, I'd suggest bringing this up in the Mathematics Stack Exchange. English doesn't require rigorous referentiality for expressions to work, as nouns do not necessarily refer to "definitive object[s]" but rather can be signifiers for abstract concepts.
– TaliesinMerlin
22 hours ago
@Visiting_Mathematician A variable is a label that is assigned to a property which can take many values. If a letter takes only one value it's not a variable, it's a constant. A good example of a variable is velocity, often given the label "v". If v is defined as the velocity of a ball thrown vertically upward its value starts off high, decreases to zero then increases as the ball falls back. There is no number which expresses all those instantaneous velocities but they are all valid values of v.
– BoldBen
20 hours ago
|
show 1 more comment
When one says a variable varies, what is meant is that the value is not known in general, but that it can assume many values. When one of these values is assumed (as in Let x be the number 2.), then that is the value of x until further notice, when it might assume another value or be undefined again.
– John Lawler
yesterday
I don't understand why you are assuming that "x" has to refer to a fixed quantity. A variable is literally a quantity that varies or is assumed to vary because the value is unknown. So 1 is 1, but x may change due to a function or other situation, and x may refer to a range of values (for all x in the set of integers...) So are you asking about how English usage within mathematics treats the variable, or how the variable is defined?
– TaliesinMerlin
yesterday
@TaliesinMerlin I am uneasy with the notion of a 'variable quantity' in mathematics because it would be hard, if not impossible, to give a rigorous definition of such a thing. I am trying to interpret the occurrence of x in a sentence as a name for a definitive object, much like how the pronoun 'it' can function as a proper noun in context.
– Visiting_Mathematician
23 hours ago
@Visiting_Mathematician If your unease is about the semantics of a variable, I'd suggest bringing this up in the Mathematics Stack Exchange. English doesn't require rigorous referentiality for expressions to work, as nouns do not necessarily refer to "definitive object[s]" but rather can be signifiers for abstract concepts.
– TaliesinMerlin
22 hours ago
@Visiting_Mathematician A variable is a label that is assigned to a property which can take many values. If a letter takes only one value it's not a variable, it's a constant. A good example of a variable is velocity, often given the label "v". If v is defined as the velocity of a ball thrown vertically upward its value starts off high, decreases to zero then increases as the ball falls back. There is no number which expresses all those instantaneous velocities but they are all valid values of v.
– BoldBen
20 hours ago
When one says a variable varies, what is meant is that the value is not known in general, but that it can assume many values. When one of these values is assumed (as in Let x be the number 2.), then that is the value of x until further notice, when it might assume another value or be undefined again.
– John Lawler
yesterday
When one says a variable varies, what is meant is that the value is not known in general, but that it can assume many values. When one of these values is assumed (as in Let x be the number 2.), then that is the value of x until further notice, when it might assume another value or be undefined again.
– John Lawler
yesterday
I don't understand why you are assuming that "x" has to refer to a fixed quantity. A variable is literally a quantity that varies or is assumed to vary because the value is unknown. So 1 is 1, but x may change due to a function or other situation, and x may refer to a range of values (for all x in the set of integers...) So are you asking about how English usage within mathematics treats the variable, or how the variable is defined?
– TaliesinMerlin
yesterday
I don't understand why you are assuming that "x" has to refer to a fixed quantity. A variable is literally a quantity that varies or is assumed to vary because the value is unknown. So 1 is 1, but x may change due to a function or other situation, and x may refer to a range of values (for all x in the set of integers...) So are you asking about how English usage within mathematics treats the variable, or how the variable is defined?
– TaliesinMerlin
yesterday
@TaliesinMerlin I am uneasy with the notion of a 'variable quantity' in mathematics because it would be hard, if not impossible, to give a rigorous definition of such a thing. I am trying to interpret the occurrence of x in a sentence as a name for a definitive object, much like how the pronoun 'it' can function as a proper noun in context.
– Visiting_Mathematician
23 hours ago
@TaliesinMerlin I am uneasy with the notion of a 'variable quantity' in mathematics because it would be hard, if not impossible, to give a rigorous definition of such a thing. I am trying to interpret the occurrence of x in a sentence as a name for a definitive object, much like how the pronoun 'it' can function as a proper noun in context.
– Visiting_Mathematician
23 hours ago
@Visiting_Mathematician If your unease is about the semantics of a variable, I'd suggest bringing this up in the Mathematics Stack Exchange. English doesn't require rigorous referentiality for expressions to work, as nouns do not necessarily refer to "definitive object[s]" but rather can be signifiers for abstract concepts.
– TaliesinMerlin
22 hours ago
@Visiting_Mathematician If your unease is about the semantics of a variable, I'd suggest bringing this up in the Mathematics Stack Exchange. English doesn't require rigorous referentiality for expressions to work, as nouns do not necessarily refer to "definitive object[s]" but rather can be signifiers for abstract concepts.
– TaliesinMerlin
22 hours ago
@Visiting_Mathematician A variable is a label that is assigned to a property which can take many values. If a letter takes only one value it's not a variable, it's a constant. A good example of a variable is velocity, often given the label "v". If v is defined as the velocity of a ball thrown vertically upward its value starts off high, decreases to zero then increases as the ball falls back. There is no number which expresses all those instantaneous velocities but they are all valid values of v.
– BoldBen
20 hours ago
@Visiting_Mathematician A variable is a label that is assigned to a property which can take many values. If a letter takes only one value it's not a variable, it's a constant. A good example of a variable is velocity, often given the label "v". If v is defined as the velocity of a ball thrown vertically upward its value starts off high, decreases to zero then increases as the ball falls back. There is no number which expresses all those instantaneous velocities but they are all valid values of v.
– BoldBen
20 hours ago
|
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When one says a variable varies, what is meant is that the value is not known in general, but that it can assume many values. When one of these values is assumed (as in Let x be the number 2.), then that is the value of x until further notice, when it might assume another value or be undefined again.
– John Lawler
yesterday
I don't understand why you are assuming that "x" has to refer to a fixed quantity. A variable is literally a quantity that varies or is assumed to vary because the value is unknown. So 1 is 1, but x may change due to a function or other situation, and x may refer to a range of values (for all x in the set of integers...) So are you asking about how English usage within mathematics treats the variable, or how the variable is defined?
– TaliesinMerlin
yesterday
@TaliesinMerlin I am uneasy with the notion of a 'variable quantity' in mathematics because it would be hard, if not impossible, to give a rigorous definition of such a thing. I am trying to interpret the occurrence of x in a sentence as a name for a definitive object, much like how the pronoun 'it' can function as a proper noun in context.
– Visiting_Mathematician
23 hours ago
@Visiting_Mathematician If your unease is about the semantics of a variable, I'd suggest bringing this up in the Mathematics Stack Exchange. English doesn't require rigorous referentiality for expressions to work, as nouns do not necessarily refer to "definitive object[s]" but rather can be signifiers for abstract concepts.
– TaliesinMerlin
22 hours ago
@Visiting_Mathematician A variable is a label that is assigned to a property which can take many values. If a letter takes only one value it's not a variable, it's a constant. A good example of a variable is velocity, often given the label "v". If v is defined as the velocity of a ball thrown vertically upward its value starts off high, decreases to zero then increases as the ball falls back. There is no number which expresses all those instantaneous velocities but they are all valid values of v.
– BoldBen
20 hours ago