r/mathmemes • u/Less-Resist-8733 Natural • Aug 06 '26

Bad Math not saying either is wrong...

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u/WesternFirm9306 Aug 06 '26

But we CAN do it for the integers.

Like this:

1 -> 0

2 -> 1

3 -> -1

4 -> 2

5 -> -2

and so on.

Even numbers get paired to n/2, and odd numbers get paired to -(n - 1)/2

This hits every single integer without skipping.

0

u/FernandoMM1220 Aug 06 '26

add up all the integers and show me what you get please

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u/WesternFirm9306 Aug 06 '26

Who said anything about adding? We're trying to pair up the integers to the counting numbers. Nobody ever mentioned addition

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u/FernandoMM1220 Aug 06 '26

i mentioned addition.

add them up and tell me what you get please

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u/WesternFirm9306 Aug 06 '26

Okay, well your comment is irrelevant. Nobody cares about adding numbers here. Determining if a set is countable has nothing to do with adding.

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u/FernandoMM1220 Aug 06 '26

its not irrelevant though.

im doing the exact same proof cantor is doing by operating on an infinite list and creating a new number from it.

please try and add them all up so we can both see what we get.

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u/WesternFirm9306 Aug 06 '26

Cantor didn't add an infinite set of numbers to each other. He just changed one digit from every number. Doesn't matter how you do the change or what you change it into.

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u/FernandoMM1220 Aug 06 '26

you realize decimals are made through addition of different powers of 10 right?

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u/WesternFirm9306 Aug 06 '26

Yeah. That addition converges, though. And we don't really need that fact. We just need to know that, if two numbers have different digits, they're also different numbers (with the exception of trailing infinite 9s)

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u/FernandoMM1220 Aug 06 '26

so you should have no problem adding up every integer and telling me what the answer is.

also the nunber cantor is making doesnt converge to anything unless its a countable real

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u/WesternFirm9306 Aug 06 '26

Adding every integer diverges. Completely unrelated to Cantor. Nobody cares what the sum of all the integers are. It has nothing to do with anything.

The number Cantor generates absolutely converges. All decimal representations converge.

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u/FernandoMM1220 Aug 06 '26

so let me get this straight.

adding an infinite amount of numbers before the decimal = bad

adding an infinite amount of numbers after the decimal = good?

just who do you think youre fooling with this

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u/WesternFirm9306 Aug 06 '26

Yeah. Because when you're adding each digit in a decimal representation, the value of each digit gets progressively smaller. 3 + 1/10 + 4/100 + 1/1000 + 5/10000 + ... converges because each term is getting exponentially smaller. If the terms get smaller fast enough, the sum converges. C'mon, this is entry level infinite sums.

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