Continuum Hypothesis is false.

Question

parthkohli · Answer

There is a bijection between the set of all decimal numbers and all whole numbers.$$0.00000000001\mapsto 1$$$$0.00000020000\mapsto 2$$We can do this for all whole numbers.

parthkohli · Answer

How can there be different infinities? I find the argument completely pointless. What do you think?

unklerhaukus · Answer

well there are different infinities

parthkohli · Answer

@UnkleRhaukus How do you say that? If you say that the set of whole numbers is less than the set of decimal numbers, I'd just add one to the number of whole numbers you claimed to have shown and I'd prove it wrong.

parthkohli · Answer

Try it, make the set of whole numbers which you believe has infinite elements. It'd still be a subset of the set of whole numbers, right?

unklerhaukus · Answer

http://www.numberphile.com/videos/countable_infinity.html

parthkohli · Answer

OK, I think it'd be bad to challenge such conjectures. Closing...

unklerhaukus · Answer

have you watched the whole video ?

shubhamsrg · Answer

Well, I was reading this and could not understand most of it. But I feel it might help you guys . http://en.wikipedia.org/wiki/Continuum_hypothesis

shubhamsrg · Answer

Discussion about its validity is made there which am trying to grasp.