Should infinity be removed from mathematics? Watch

Karma Peny
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I studied mathematics at school and as part of my computing degree, but I never felt at ease with the concept of infinity. Recently I gave the matter more thought and I reached the conclusion that infinity is not a valid concept.

Of all the areas of mathematics that I have encountered (school-level set theory, calculus, geometry, probability and so on) I could find no valid reason for using infinity. For me, its intangible nature creates mysticism where I would prefer precision and clarity. To address this, I wrote an article suggesting how we could start to remove infinity from these areas of mathematics (see: www.extremefinitism.com/background).

Infinity causes problems that do not exist without it. For example, if we accept the infinite set of all natural numbers actually exists {1, 2, 3, 4…}, what is the percentage of odd numbers in this set?

The obvious answer of 50% is problematic because it implies an even number of elements whereas infinity is supposedly neither odd nor even. Another option is to say the cardinality of the set of all odd natural numbers is exactly the same as the cardinality of all natural numbers, which is far from a satisfactory answer.

Without infinity we can simply say the percentage of odd numbers in the first n natural numbers is 100*floor[(n+1)/2)]/n where n>=1 (note that 'floor' means 'round down'). Without infinity we can say this is a complete solution for all natural numbers. Without infinity we no longer have any problems.

There is a nice bullet-point summary of the main problems with infinity (as a mathematical concept) at the end of this article:
http://www.extremefinitism.com/blog/...f-the-problem/

I am very interested to hear other people's ideas on how to remove infinity from mathematics, or possibly why it should not be removed at all. The more opinions I can get about this subject the better. Many thanks in advance.
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TeeEm
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(Original post by Karma Peny)
I studied mathematics at school and as part of my computing degree, but I never felt at ease with the concept of infinity. Recently I gave the matter more thought and I reached the conclusion that infinity is not a valid concept.

Of all the areas of mathematics that I have encountered (school-level set theory, calculus, geometry, probability and so on) I could find no valid reason for using infinity. For me, its intangible nature creates mysticism where I would prefer precision and clarity. To address this, I wrote an article suggesting how we could start to remove infinity from these areas of mathematics (see: www.extremefinitism.com/background).

Infinity causes problems that do not exist without it. For example, if we accept the infinite set of all natural numbers actually exists {1, 2, 3, 4…}, what is the percentage of odd numbers in this set?

The obvious answer of 50% is problematic because it implies an even number of elements whereas infinity is supposedly neither odd nor even. Another option is to say the cardinality of the set of all odd natural numbers is exactly the same as the cardinality of all natural numbers, which is far from a satisfactory answer.

Without infinity we can simply say the percentage of odd numbers in the first n natural numbers is 100*floor[(n+1)/2)]/n where n>=1 (note that 'floor' means 'round down'). Without infinity we can say this is a complete solution for all natural numbers. Without infinity we no longer have any problems.

There is a nice bullet-point summary of the main problems with infinity (as a mathematical concept) at the end of this article:
http://www.extremefinitism.com/blog/...f-the-problem/

I am very interested to hear other people's ideas on how to remove infinity from mathematics, or possibly why it should not be removed at all. The more opinions I can get about this subject the better. Many thanks in advance.
go on purists... have a go

( I sit on the fence as I am very busy tonight so I would not mind reading the debate...)
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The_Last_Melon
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Infinity is a useful concept as a result of the question: "What happens when the denominator approaches zero?"
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