Which set is bigger, A = n or B = 2n, and n tends to infinity

>>8450649
This reminds me: I once took a philosophy class wherein the grad student leading the discussion section claimed that the set of integers was "twice as big" as the set of even integers.

keep your pedophile cartoons and bring more from /a/

>>8450651
>This reminds me: I once took a philosophy class wherein the grad student leading the discussion section claimed that the set of integers was "twice as big" as the set of even integers.


Yeah this is a common misconception. I can map the integers to the even integers with f(x)= 2x. similarly I can map the even integers to the integers by f(x)=x/2. It's a bijection so the idea that one has more elements than the other is ridiculous.

>>8450649
what you wrote doesn't make sense, if you meant the sets A={1,2,3, ... } and B={2,4,6, ... } then they have the same size.

>>8450741
What if you're the one not making sense

>>8450741
>>8450745
Oh snap

not all infinities are made equal

>>8450649
They are equal.

A more interesting question would be about countable and uncountable infinities, such as rational vs irrational numbers. When comparing sets of infinite numbers it's all about how you can count them because it makes no sense to determinate which one is bigger at the end since there is no limit to stop them from growing.

>>8450649
You mean A∈{n} or B∈{2n} as n->inf?

Well, since infinity is not actually a stable number, constants go away. Cause you can't say infinity plus 1, it's still infinity.

>>8450649
Feel free to shit down my gaping throat if I'm wrong, but from what I understand, Infinity is not a set value. It encompasses all possible values, so it can't be compared to something in relation to size, quantity, etc. The same logic applies to countable infinities; the idea of it, outside the language of mathematics, remains simply that. An intangible idea. I'm trying not to sound like some pseudo-intellectual philosophy student sitting in a Seattle coffee shop, so let me try to wrap this up. Infinity, and countable infinities, are ideas that can only be articulated through math. Trying to relate them to aspects of human perception is really not possible, because the things we are able to observe and compare ultimately abide by set physical laws. The idea of a limitless is something incomprehensible, and as such, indescribable, to a mind that has a limited operating system

>>8450649
Both are infinite, but the cardinality of set A is bigger than that of set B. Btw guys, did you know that 1 + 2 + 3 ... = -1/12? xD

>>8450829
>Feel free to shit down my gaping throat
I would if I could honey ;)

>>8450831
>the cardinality of set A is bigger than that of set B
So you're basically saying that A > B

In terms of inclusion, B is included in A, so if that's what you meant by by 'bigger', then A is bigger than B.
But there is a one to one match between the two sets, so if by 'bigger' you meant their elements can be matched one to one uniquely, then they are the same size.

>>8450649
How to blow an undergrad mathematicians mind.
There is a rational number between any two irrational numbers.
There is an irrational number between any two rational numbers.

There set of irrational numbers is infinitely bigger than the set of rational numbers.

>>8451028
There is a rational number between any two irrational numbers.
There's no irrational number between 3/2 and 3/2

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>>8451048
>There's no irrational number between 3/2 and 3/2

No shit Sherlock! They are the same number!!!

>>8451048
How retarded do you have to be to even think of this?

>>8451050
>>8451067

Did you read what I failed at quoting?
> There is an irrational number between any two rational numbers.
It's wrong, I was pointing out a counterexample
Both 3/2 and 3/2 are rational numbers.
But between them is no irrational number

>>8450649
Neither the sets are the same. As in literally identical.

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>>8451078

3/2 and 3/2 are NOT two rational numbers they are ONE (same) number. "One" is not same as "Two".

Either you are certifiable retarded or a post graduate PhD in Mathematics.

>>8451084
You new to mathematics then?
there's a reason we use words such as distinct.
> The sum of two rational numbers is a rational

>>8451086
You are correct.
Two DISTINCT numbers.

Only a mathematician would produce the same number twice and say that it is two numbers.

>>8451067
He's right

>>8450651
>>8450649
They both have the same order of infinity because you can create a 1:1 bijection between each and every item in the infinite set.

With real numbers there is no known method for creating a 1:1 bijection between all real numbers and all integers.

But there are ways to make an inexact bijection.

B = 2n obviously, except where n is one or 0.

A = 2
B = 4
A = -2
B= -4

>>8451155
>But there are ways to make an inexact bijection.

What is that even supposed to mean.

>>8451114
He's a pedant

>>8451157
It means you can make something that is approximate to a bijection and mostly works for a subset.

If a true bijection were a color photograph, an inexact bijection would be a grey-scale photograph. It might not be what you wanted but it would work.

Also for ordering real numbers consider a binary number 5 = 101. You can add fractions so 5/8 = 1/2 + 1/8 = 0.101. Giving you 5 & 5/8 = 101.101

You can enumerate any binary compound fraction of a certain length and continue to extend the lengths towards infinity. However you have holes of inexpressible numbers between any finite length number.

>1.33 repeating because you can't put infinite 3s in decimal
So at what point in this algorithm could you express 1 and 1/3rd in decimal? Never.

Depends what you mean by bigger.
They have the same cardinality (countable).
They have the same measure (zero).
They are both not dense in R.

>>8451155
>There is no known method
That makes it sound like the question is still open. It is known that making a bijection is impossible.

>>8451176
>it is le impossible to create a symbolic method to order all real numbers into a integer bijection
Our algorithmic and logical abilities are have been shown insufficient through mathematical proof, that is not the same as impossible.

A new mathematical system might be discovered/invented with the capability, but this is trying to unify dark matter/energy, special relativity and quantum mechanics using only classical physics.

>>8451186
Hahaha this post made me laugh.

to be quite frank i find the consept of infinity absurd; the world around us is made out of small planck particles, thoose particles are the very foundation of the universe. i.e since the universe is finite e.g. it is not infinite. it would not make much sense to claim the fact that an idea can be represented via infinity since the universe itself is not.

What if it's the same problem but with limit instead of set?
limit of f(x)=x as x -> inf
vs
limit of g(x)=2x as x -> inf

>>8451245
Both infinity and the limit doesn't exist for either

>>8450649
How are those definitions of sets?

>>8450649
A and B have the same cardinality, but A has a greater measure than B.

Whether either of those answers what you mean is left to the philosopher as an exercise.

>>8450884
If he wasn't being sarcastic yeah

>>8450649
Logical operators cannot be applied to infinity. However let's say you divide the right sides by n. Then B would be bigger.

>>8451084
I'm using that book currently. it's pretty good