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/sci/ - Science & Math

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1369190 No.1369190 [Reply] [Original]

>My face when the infinity between 0 and 1 is bigger than the infinity of positive integers

What the fuck man, first you tell me infinity is a concept and can't be measured, now you tell me some infinities are bigger than others? Somebody please make sense of this for an intrigued non-mathematician.

>> No.1369204

The infinity between 0 and 1 is non countable.
The infinity of positive integers is countable.

non-countable > countable

>> No.1369208

Cantor and his diagonal lines.

>> No.1369209

are you refering the cardinality of the set of rational numbers between 0 and 1? If so then it is the same size as the cardinality of the set of positive integers

>> No.1369216

>>1369204
That doesn't mean anything. They are both infinite.

>> No.1369236

>>1369216

But they have different degrees of infinity.

>> No.1369250

yeah stephen hawking is cool to infinity

carl sagan is cool to a whole nother degree of infinity

>> No.1369256

>>1369236
Citation pls, it's not relevant imho because infinity isn't a number, it's a stand-in for boundless. You can have a line infinite in both directions or a line infinite in one direction, but you can't have more or less infinity than infinity because it's not a real quantity.

>> No.1369264

>>1369256
FUCK YOU LEARN TO MATH.

But here - http://mathworld.wolfram.com/CountablyInfinite.html

>> No.1369265

>>1369256

http://mathchaostheory.suite101.com/article.cfm/degrees_of_infinity

>> No.1369302

>>1369265
This confirms what I said, the two are categorically different but not quantitatively.

>> No.1369323
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1369323

Pic related

>> No.1369328

>>1369323
Thanks creepy skin condition window guy... I understand now.

>> No.1369346

>>1369323
This is a surprisingly good explanation. Especially the first bubble.

>> No.1369352

>>1369302
your idea of infinity is just confused

Infinity can be used in different situations. It can be used in limits and such, like you are probably thinking of it. It can also be used as the size of a set, in which case the terms countably and uncountably infinite have meaning and are certainly different.

>> No.1369369

>>1369352
My idea's not confused, it's that "bigger" is a bad word to use in this context. There's a difference between countable and uncountable, but it's not in amount.

That said, I'm winging it here because I don't study set theory, which is what I figured out halfway through was what was being talked about.

>> No.1369375

>>1369323
+1

>> No.1369394

>>1369369
>but it's not in amount.
Except it is. See:
>>1369323

>> No.1369402

>>1369394
Except that's wrong.

>> No.1369426

>>1369402
No reasoning with you, then. Enjoy being ignorant.

>> No.1369430

"The Cantor diagonal method, also called the Cantor diagonal argument or Cantor's diagonal slash, is a clever technique used by Georg Cantor to show that the integers and reals cannot be put into a one-to-one correspondence"

"A and B are in one-to-one correspondence" is synonymous with "A and B are bijective."

"A map is called bijective if it is both injective and surjective."

"Let f be a function defined on a set A and taking values in a set B. Then f is said to be an injection (or injective map, or embedding) if, whenever f(x)=f(y), it must be the case that x=y. Equivalently, x!=y implies f(x)!=f(y). "

"Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for which b=f(a). "

Sets. Not quantities. Different. Not bigger or smaller except one fits in the other, but you're not counting so it's still not a quantity.

>> No.1369431

>>1369426
Stick with your fallacy of equivocation then.

>> No.1369435

>>1369256
within your infinity there is an infinite number of infinities that make it up.

>> No.1369436

>>1369430

Except a one-to-one correspondence between sets means that they're the same size.

>> No.1369443

>>1369436
Not according to that link :-/

Look, if you want to say that by those definitions non-countable is bigger than countable, that's perfectly reasonable, but that's not the non-mathematician's definition of bigger, hence the confusion. That's all I'm getting at.

>> No.1369452

>>1369443

http://en.wikipedia.org/wiki/One_to_one_correspondence#Bijections_and_cardinality

>> No.1369470

>>1369452
Reading now, this is a better explanation than that Wolfram site.

>> No.1369560

http://en.wikipedia.org/wiki/Countable_set#Very_gentle_introduction

This makes a lot more sense, and implies what I was saying, that cardinality and "size" are not equivalent. It gives an example of one-to-one correspondence that does not match size.

"However, it turns out that the number of odd integers, which is the same as the number of even integers, is also the same as the number of integers overall."

Or am I making a mistake here?

>> No.1369609

>>1369323

What a mind fuck...

>> No.1370220

>>1369609

Meh. I used to think about that stuff when I was younger, I'm just happy it was formalized.