which set is bigger?

Question

A = {1,2,3,............................................... }

B = {2,4,6,................................................ }

both are infinite set!!!

which is bigger

i know the answer, but i thought it would be good question to ask!

ps: yes most of you are right! but I was looking for function mapping to prove this!!!

thank you for your response

ps: the guy who wrote:
need help with homework! ha! buddy finnished a everything.....pretty ignorant view!

ok...i wont go too much detail
but here is the idea

it may seem that B is smaller set...because it starts later than A

but let f be a function

let a be a value of set A and let b be a value for B

f(2a) = b

essentially we can map all the element of a into b

so the set are same!!!

ANSWER IS: THEY ARE SAME, FOR DETAILS LOOK ABOVE, ITS THERE

ORACLE YOU MUST BE ..NEVER MIND!

BLUE MAN !!! YOU ARE RIGHT!!!

EDWARD-----> LOOK AT MY IDEA! IT IS NOT COMPLICATED

Answer 1

Both sets have cardinality aleph null.
(Meaning there are in one to one correspondence with the set of natural numbers. Set A is just the natural numbers. Set B are all the natural numbers multiplied by 2).
Check out Cantor.

Answer 2

There are several levels of infinity. Your's is level 1. and both or yours are equal. For each item in A there is a corresponding B.

The set of rational numbers is also a level 1 infinity.

A level 2 infinity is the set of all numbers including irrational numbers.

An example of level 3 of infinity is this:

Points A and B are on a 2 dimensional graph (a map). The number of paths from A to B represents a level 3 infinity.

That's all I can remember, but I believe there are even higher levels.

Answer 3

These 2 sets have the same cardinality, because
we can set up a 1-1 correspondence between them
via the map n --> 2n. The cardinality of each is
the smallest infinite cardinal number, aleph_0.

Answer 4

they're both the same size, as one can match each element in the first set to a corresponding element of the second set. all those people who said that infinite sets are equal in size are not necessarily correct. there are different orders of infinity. for example, the set of natural numbers, though infinite, has less elements than the set of real numbers. that is, the real numbers are on a higher order of infinity than the set of natural numbers.

Answer 5

f:A -> B by f(x) = 2x
g:B -> A by g(x) = x/2

Now you need to check that fg = gf = the identity map, which shows that both are bijections, and you need to check to see if f and g are both well defined.

That shows that both have the same number of elements, even though B is a proper subset of A. Actually A can also be mapped 1-1 onto a proper subset of B by h(x) = 4x.

Answer 6

Arrrgh... eyes got problem...
Got my set A different from yours.
=========================

A = {x in set of positive integers : x mod 2 = 1}
B = {x in set of positive integers : x mod 2 = 0}

Let x be an element of A.
For all x, (x+1) mod 2
= ((x mod 2) + 1) mod 2
= (1+1) mod 2
= 2 mod 2
= 0,
so x+1 is an element of B.
Thus, |A| <= |B|.

Let y be an element of B.
For all y, (y-1) mod 2
= ((y mod 2) -1) mod 2
= (0 - 1) mod 2
= -1 mod 2
= 1,
so y-1 is an element of A.
Thus, |B| <= |A|.

So, |A| = |B|.

Answer 7

set B is bigger than set A. Because though these both set r infinite.the nos. in set A have the difference of 1 but in set B the nos have the difference of 2.hence , whatever the last no. would be considered in set A ,the no.in set B would be greater than the no. in set A.
hence, last no.in set A suppose, 3 is the last no. considered in set A then 6 is the last no. occurred in the set B.

Answer 8

The sets are the same but the numbers after adding them up at end would equate to B being the winner!

Answer 9

First of all, define "bigger". If you mean the cardinal, then both sets are in equal "size". If you meant something else, specify it.

Answer 10

I think that set "A" is bigger.Both sets are infinite but set"B" is set of even niumbers and set"A" is a set of unviversal numbers(which includes all numbers) so thts whay i think tht set"A" is bigger.its a good question.