Submitted by [deleted] t3_z9436g in Showerthoughts
splitlikeasea t1_iyf5exa wrote
Reply to comment by Dr0110111001101111 in There's the same amount of numbers between -∞ to 0 and -∞ to ∞ by [deleted]
I think this is a bit complex for someone who made such a comment. Basically: If you slice up as part of your number and you get a finite amount of numbers, it's a countable infinity.
Take 15-30 range from -infinity to +infinity range of integes and you have finite amount of integer.
If you slice up a part of your numbers and there is still infinite amount of numbers in it, it's an uncountable infinity.
Take 1-2 on rational set and pick any part of it, say from 1.2 to 1.3. there are are infinite amount of numbers you can choose as you can just add another decimal to end.
Uncountable infinities are infinitely denser than countable infinities. And since every uncountable infinity is infinitely dense, all of them are incomparable to each other when it comes to size. Infinity is not a number but a virtual concept so it can go into unimaginable areas.
Dr0110111001101111 t1_iyf6hvi wrote
How would you "slice up" the set of rationals and get a finite set?
[deleted] OP t1_iyf8ley wrote
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