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/sci/ - Science & Math

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4450319 No.4450319 [Reply] [Original]

Is the number of integers odd?

1 to infinity can be either even or odd, same with negative infinity to -1. The intervals are symmetric about zero so their evenness or oddness is the same and when added necessarily make an even number, that plus zero makes it odd.

does this sound possible? I'm far from a mathematician, any opinions or insults appreciated

>> No.4450332

shut the fack up

>> No.4450343

>>4450332
I will soon enough.

Does the concept of an even or odd infinity sound ridiculous to anyone else? I guess one could say there is a one-to-one correspondence of positive to negative integers, so there are as many positive integers as there are negative. So the amount of integers is 2*(amount of positive integers) + 1 (for zero)

anyone know set theory?

>> No.4450344

The fuck? it's neither or or even, it's just infinity. You're thinking of infinity as a number when it's not.

>> No.4450352
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4450352

>>4450343
>So the amount of integers is 2*(amount of positive integers) + 1 (for zero)

congrats, you just showed 2 * infinity + 1 = infinity. You didn't solve shit.

>> No.4450357

>>4450319
that's like saying 1-1+1-1... = 0

>> No.4450360

Can we agree 2*(anything) is an even number?
What would exclude 2*(infinity)?

>> No.4450361

>>4450360
INFINITY ISN'T A NUMBER SO STOP TREATING IT LIKE ONE.
/rage
/thread

>> No.4450362

>>4450357
Yes.
0 is an even number, plus 1 makes it 1 which is odd?

>> No.4450365

>>4450361
Infinity is indeed a number, it denotes a quantity, real or not.

>> No.4450370

>>4450362
...
the point is that you can't reduce it to a number, so stop trying

>> No.4450379

>>4450370
Are you trying to argue 2+2+2+2+2..... is not an even number?

>> No.4450381

>>4450379
Just stop

>> No.4450382

>>4450343
>>4450319

Go study elsewhere philosofaggot

>> No.4450386

>>4450319
The notions of "even" and "odd" only make sense for natural numbers, not infinities. Also, you can't compare sizes of infinities like that consistently. For example, consider that we can match 1 up with 4, 3 with 6, 5 with 8, 7 with 10, etc, but we are left with two even numbers left over, not just one.

>> No.4450389

Asking if infinity is even or odd is like asking if 2.5 is even or odd. It's neither. The question makes no sense.

>> No.4450390

>>4450382
Mathematics and philosophy (logic, epistemology) are inextricably linked.

What is wrong with my argument? If any finite multiplication of 2 is even why wouldn't an infinite one be even as well?

>> No.4450396

>>4450390
>whats wrong with my argument?
You have no argument because you don't even know the definitions.
"x is even" is equivalent to the statement "there exists an integer y such that x = 2 * y". Thus, it only applies to integers.

>> No.4450398

>>4450396
thank you my good man, you've cleared that up for me. We're done here

>> No.4450404

The set of integers is countable, that means it has as many members as the natural numbers but what you propose to show is that it has almost twice the amount of members.

>> No.4450416

>>4450404
I do believe that was what I was looking for.
Thanks

>> No.4450426 [DELETED] 

test

>> No.4450434
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4450434

No one in this thread understands math

>> No.4450442

>>4450344
>>4450361
>>4450370
Look at these fucking retards.

Please guys, please stop being uneducated dumbfucks. Do /sci/ and the world a favor and kill yourself.
"Infinity is not a number" is the biggest bullshit one can say.
Infinity is not a REAL number. That's it. Learn the fucking difference.

>> No.4450642

>>4450442
>Infinity is not a REAL number.
Infinity is not any kind of number, Cantor.
Lrn2aleph-null

>> No.4450656

lim (x -> inf) x mod 2 doesn't converge.

so neither.

Although interestingly, it's trivial to see infinity can't be even, because it would imply a finite number of primes.

>> No.4450660

>>4450656
>Although interestingly, it's trivial to see infinity can't be even, because it would imply a finite number of primes.
pardon my dumbness, but why would it imply that?

>> No.4450879

>>4450642
Then define "number" in a manner that excludes infinity and is compatible with all definitions of special cases of numbers.

I fucking dare you, retard.

>> No.4450896

>>4450642
>mfw ordinal numbers