Question

I want to pose a simple question.

Answer 1

There are infinite numbers and infinite even numbers , so does it mean that the set of all numbers has the same elements as the set of even numbers?

Answer 2

what is you question

Answer 3

ITS ON my profile

Answer 4

It is not a part of my homework or anything , the question is already asked above.
I wantted your views about the statement

Answer 5

i think so

Answer 6

Yes @No.name

Answer 7

but in 1-10 there are 10 numbers and 5 even numbers

Answer 8

the set of even integers and the set of all numbers (I guess you mean complex) have a different cardinality.
The even integers are countable where as the complex numbers aren't countable.

Answer 9

If somebody does not agree with my question let me know , i will present a simple proof

Answer 10

i mean not imaginary numbers

Answer 11

Still the real numbers are uncountable.

Answer 12

so the even numbers , but they seem to be unequal

Answer 13

whats the answer

Answer 14

even though both are uncountable , i hope you got what i mean

Answer 15

Well see this everybody :-
http://www.youtube.com/watch?v=UPA3bwVVzGI&list=PLOGi5-fAu8bEIw_xkj1FgKr7QY_Sahswy&index=4

Answer 16

What? I said the even integers are countable. The real numbers aren't.

Answer 17

even numbers are not countable they are infintely present in real numbers

Answer 18

where the set of real numbers is itself infinite

Answer 19

If we can find a bijection between the even integers and the integers, then that means the even integers are countable. And they are because f: integer->even integers defined by f(x)=2x.

Answer 20

Okay , that video just proves my statement incorrect
and it says
even numbers = all real numbers
this is somewhat bizzare but see the video in free time

Answer 21

the video should should begin with "there are as many even numbers as all the integers"

Answer 22

The set of real numbers is not countable.
A subset of the real numbers is the set (0,1) and we can not list all the numbers between 0 and 1 so there is not a bijection between the set of integers ant set (0,1) so therefore (0,1) is uncountable. And the real numbers are uncountable. And the complex numbers are uncountable.

Answer 23

Yeah actually
infact all subset of real numbers has the same elements as real numbers

Answer 24

Not not all subsets...

Answer 25

real number set*

Answer 26

the set of integers is a subset of the real numbers

Answer 27

yes all even fractions

Answer 28

what is an even fraction?

Answer 29

it is tough to believe though

Answer 30

no not even or odd
all fractions

Answer 31

lol @No.name you seem too excited about the video and numbers that you're inventing new terminology ;p

Answer 32

sry am i

Answer 33

my actual question is
Is one infinity greater than other infinity?

Answer 34

indeed it is tough to believe but it will make sense if we thing a bit using the known infinite geometric series. why is below true :

\(\large \sum \limits_{n=1}^{\infty} \dfrac{1}{2^n} = \sum \limits_{n=1}^{\infty - M} \dfrac{1}{2^n} \)

Answer 35

M is ?

Answer 36

M could be ANY number, large/small

Answer 37

```
my actual question is
Is one infinity greater than other infinity?
```
using bijection stuff, it becomes easy to see why all countable infinite sets like : even numbers / whole numbers / integers have the same size

Answer 38

i have to learn bjection , or is it a 1 sec concept

Answer 39

i also don't have much exposure into fascinating infinities concept...
im reading this at the moment
http://math.stackexchange.com/questions/341605/as-many-even-numbers-as-natural-numbers

Answer 40

wow , i will read as much as i can get from that
but see the video , it is good

Answer 41

ACtually george cantor proved it using set theories

Answer 42

watching it

Answer 43

out from my imagination power , too baffled right now

Answer 44

but still i am convinced

Answer 45

how baffling
the decimal is a subset of whole numbers ,
still contains more elements than whole numbers.

Answer 46

Infinity i believe is continously expanding i believe

Answer 47

and the lesser infinty approaches a more greater infinity than it, that's what i think

Answer 48

so as georg cantor think to put a infinity between two infinities , it is impossible
since you can't stop the infinity that is continuously creating subsets within it
this awesome stufffff!

Answer 49

This video is even more amazing
http://www.youtube.com/watch?v=Uj3_KqkI9Zo
Not watching more videos my mind is already blown by this concept