Is it mathematically wrong to say “infinite number”?
I often hear the phrase "an infinite number of..." in mathematics. Is this phrase mathematically ungrammatical, since infinity is not a "number"?
I'm sure some people will say that whether this phrase is right or wrong is a matter of opinion or taste, or that if people are saying it and know what it means, then who's to say it's wrong. Fine. I'm just curious about how most mathematicians feel about it. Could it lead to conceptual pitfalls? Or should the most modern and broad notion of "number" include "infinity" as a member?
terminology
asked 42 mins ago
WillG
44938
add a comment |
I often hear the phrase "an infinite number of..." in mathematics. Is this phrase mathematically ungrammatical, since infinity is not a "number"?
I'm sure some people will say that whether this phrase is right or wrong is a matter of opinion or taste, or that if people are saying it and know what it means, then who's to say it's wrong. Fine. I'm just curious about how most mathematicians feel about it. Could it lead to conceptual pitfalls? Or should the most modern and broad notion of "number" include "infinity" as a member?
terminology
asked 42 mins ago
WillG
44938
4
"Infinitely many..." is more idiomatic.
– Lord Shark the Unknown
40 mins ago
1
When people say that infinite is not a number, it simply means that there is no way to reconcile the naive notion of 'positive/negative infinity' and the algebraic rules over the real numbers. In other words, for other purposes one can actually come up with rigorous theories dealing with infinities. Infinite cardinals are quintessential examples.
– Sangchul Lee
24 mins ago
add a comment |
I often hear the phrase "an infinite number of..." in mathematics. Is this phrase mathematically ungrammatical, since infinity is not a "number"?
I'm sure some people will say that whether this phrase is right or wrong is a matter of opinion or taste, or that if people are saying it and know what it means, then who's to say it's wrong. Fine. I'm just curious about how most mathematicians feel about it. Could it lead to conceptual pitfalls? Or should the most modern and broad notion of "number" include "infinity" as a member?
terminology
asked 42 mins ago
WillG
44938
I often hear the phrase "an infinite number of..." in mathematics. Is this phrase mathematically ungrammatical, since infinity is not a "number"?
I'm sure some people will say that whether this phrase is right or wrong is a matter of opinion or taste, or that if people are saying it and know what it means, then who's to say it's wrong. Fine. I'm just curious about how most mathematicians feel about it. Could it lead to conceptual pitfalls? Or should the most modern and broad notion of "number" include "infinity" as a member?
terminology
terminology
asked 42 mins ago
WillG
44938
asked 42 mins ago
WillG
44938
asked 42 mins ago
WillG
44938
asked 42 mins ago
WillG
44938
asked 42 mins ago
WillG
44938
44938
4
"Infinitely many..." is more idiomatic.
– Lord Shark the Unknown
40 mins ago
1
When people say that infinite is not a number, it simply means that there is no way to reconcile the naive notion of 'positive/negative infinity' and the algebraic rules over the real numbers. In other words, for other purposes one can actually come up with rigorous theories dealing with infinities. Infinite cardinals are quintessential examples.
– Sangchul Lee
24 mins ago
add a comment |
4
"Infinitely many..." is more idiomatic.
– Lord Shark the Unknown
40 mins ago
1
When people say that infinite is not a number, it simply means that there is no way to reconcile the naive notion of 'positive/negative infinity' and the algebraic rules over the real numbers. In other words, for other purposes one can actually come up with rigorous theories dealing with infinities. Infinite cardinals are quintessential examples.
– Sangchul Lee
24 mins ago
4
4
"Infinitely many..." is more idiomatic.
– Lord Shark the Unknown
40 mins ago
"Infinitely many..." is more idiomatic.
– Lord Shark the Unknown
40 mins ago
1
1
When people say that infinite is not a number, it simply means that there is no way to reconcile the naive notion of 'positive/negative infinity' and the algebraic rules over the real numbers. In other words, for other purposes one can actually come up with rigorous theories dealing with infinities. Infinite cardinals are quintessential examples.
– Sangchul Lee
24 mins ago
When people say that infinite is not a number, it simply means that there is no way to reconcile the naive notion of 'positive/negative infinity' and the algebraic rules over the real numbers. In other words, for other purposes one can actually come up with rigorous theories dealing with infinities. Infinite cardinals are quintessential examples.
– Sangchul Lee
24 mins ago
add a comment |
1 Answer
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Infinity is not a number, as you said. However, it is a cardinality. For example, the cardinality of the naturals is $aleph_0$ and the cardinality of the reals is $aleph_1$ , basically, different sizes of infinity. Thus, although infinity cannot be considered a number, it can be used as a measure of size. Hence, it is mathematically and grammatically correct to use phrases such as 'infinitely many', or 'an infinite number of '.
answered 34 mins ago
Haran
757317
add a comment |
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Infinity is not a number, as you said. However, it is a cardinality. For example, the cardinality of the naturals is $aleph_0$ and the cardinality of the reals is $aleph_1$ , basically, different sizes of infinity. Thus, although infinity cannot be considered a number, it can be used as a measure of size. Hence, it is mathematically and grammatically correct to use phrases such as 'infinitely many', or 'an infinite number of '.
answered 34 mins ago
Haran
757317
add a comment |
Infinity is not a number, as you said. However, it is a cardinality. For example, the cardinality of the naturals is $aleph_0$ and the cardinality of the reals is $aleph_1$ , basically, different sizes of infinity. Thus, although infinity cannot be considered a number, it can be used as a measure of size. Hence, it is mathematically and grammatically correct to use phrases such as 'infinitely many', or 'an infinite number of '.
answered 34 mins ago
Haran
757317
add a comment |
Infinity is not a number, as you said. However, it is a cardinality. For example, the cardinality of the naturals is $aleph_0$ and the cardinality of the reals is $aleph_1$ , basically, different sizes of infinity. Thus, although infinity cannot be considered a number, it can be used as a measure of size. Hence, it is mathematically and grammatically correct to use phrases such as 'infinitely many', or 'an infinite number of '.
answered 34 mins ago
Haran
757317
Infinity is not a number, as you said. However, it is a cardinality. For example, the cardinality of the naturals is $aleph_0$ and the cardinality of the reals is $aleph_1$ , basically, different sizes of infinity. Thus, although infinity cannot be considered a number, it can be used as a measure of size. Hence, it is mathematically and grammatically correct to use phrases such as 'infinitely many', or 'an infinite number of '.
answered 34 mins ago
Haran
757317
answered 34 mins ago
Haran
757317
answered 34 mins ago
Haran
757317
answered 34 mins ago
Haran
757317
757317
add a comment |
add a comment |
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4
"Infinitely many..." is more idiomatic.
– Lord Shark the Unknown
40 mins ago
1
When people say that infinite is not a number, it simply means that there is no way to reconcile the naive notion of 'positive/negative infinity' and the algebraic rules over the real numbers. In other words, for other purposes one can actually come up with rigorous theories dealing with infinities. Infinite cardinals are quintessential examples.
– Sangchul Lee
24 mins ago