ParthKohli
  • ParthKohli
Continuum Hypothesis is false.
Mathematics
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SOLVED
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chestercat
  • chestercat
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ParthKohli
  • ParthKohli
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
  • ParthKohli
How can there be different infinities? I find the argument completely pointless. What do you think?
UnkleRhaukus
  • UnkleRhaukus
well there are different infinities

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ParthKohli
  • ParthKohli
@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
  • ParthKohli
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
  • UnkleRhaukus
http://www.numberphile.com/videos/countable_infinity.html
ParthKohli
  • ParthKohli
OK, I think it'd be bad to challenge such conjectures. Closing...
UnkleRhaukus
  • UnkleRhaukus
have you watched the whole video ?
shubhamsrg
  • shubhamsrg
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
  • shubhamsrg
Discussion about its validity is made there which am trying to grasp.

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