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## Main Question or Discussion Point

The program Wolfram Alpha say "True" but my friends want the Proof.

Could you help me please?

Could you help me please?

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- #1

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The program Wolfram Alpha say "True" but my friends want the Proof.

Could you help me please?

Could you help me please?

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- #2

mathman

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What is the "Probation"??? In any case, there are many different "infinities".

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I'm so sorry I mean " proof "

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many different "infinities".

So we can't find the answer for this question right?

So we can't find the answer for this question right?

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Hurkyl

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Normally, mathematicians aren't so obfuscating that they would opt to use the same word in two different ways in such a short time. And so the answer would be "obviously yes" in pretty much any instance it would come up.

In your instance, I think Mathematica uses [itex]\infty[/itex] to mean the positive infinite number in the extended real numbers.

- #7

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We know that

inf+1 = inf-----(1)

(inf+1) +1 = inf+1

from (1) replace the left (inf+1) with inf

inf+1 = inf+1

and

inf +1 - 1 = inf +1 -1

inf = inf ###

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he think about Aleph numbers in the set theory

what do you think about it?

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#6 Intelligent!!!!!!

nice to meet you .^^

nice to meet you .^^

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There is a theory of cardinal number and a theory of ordinal numbers as well.

he think about Aleph numbers in the set theory

what do you think about it?

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Hurkyl

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For the opening poster's sake, I want to point out that while there are many infinite cardinal and ordinal numbers, none of them are called "infinity". The occasional use of the noun "infinity" in that context is a historical artifact of the time before people realized those number systems had more than one infinite element -- and I don't recall ever hearing a mathematician use the word "infinity" in that way.There is a theory of cardinal number and a theory of ordinal numbers as well.

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You'd have to define divisibility for real numbers first.

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sorry, i meant integers

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Hurkyl

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What do you mean by size? Normally in that setting it's used to refer to cardinality -- and the two infinite numbers you defined really are equal.Therefore, these infinities are not equal.

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For integers those sets are actually equal in size.sorry, i meant integers

Regardless, in set theory you don't say things like size "infinity", you would say the specific cardinal. Like [itex]2^{\aleph_0}[/itex].

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I am just refering to how we would logially interpret it. Obviosly the gap between 1 and 3 is twice the size of the gap between 1 and 2What do you mean by size? Normally in that setting it's used to refer to cardinality -- and the two infinite numbers you defined really are equal.

- #19

Hurkyl

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You don't mean "logically interpret" you mean "intuit".I am just refering to how we would logially interpret it. Obviosly the gap between 1 and 3 is twice the size of the gap between 1 and 2

The problem is that you are intuiting something that is not cardinality -- but then demanding that cardinality adhere to that intuition.

In the latter case -- the size of the intervals [1,2] and [1,3] -- your intuition is that you want to measure these subset of the line with the notion of "length". Length has very little to do with cardinality -- the only relationship between the two ideas is that only sets of cardinality

(where

(I may be assuming the continuum hypothesis)

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Hurkyl you are genuis .!!

^^

^^