for any infinite cardinality there is a greater infinite cardinality — TonesInDeepFreeze
Time well spent would be to learn some mathematics rather than claiming untrue things about it. — TonesInDeepFreeze
A quick look will tell you that there are twice as many feet as there are people. You do not need to count the number of people to know this to be true; just check for amputees... — Banno
Perhaps one might argue that there is no count involved with regards to the latter and that it's just a fact that Infinity encompasses an infinite number of natural numbers. But if that's the case, then Infinity also encompasses an infinite number of possible real numbers and possible letters or possible x. But where there is no counting involved, all infinites are of the same size/quantity (or rather, infinity is one quantity as opposed to different quantities). — Philosopher19
Anyway, did someone say "beyond infinity"? — TonesInDeepFreeze
I don't believe I'm the one saying untrue things — Philosopher19
There is least infinite cardinal, which is the cardinality of the set of the infinite set of natural numbers. And there are cardinals greater than the least infinite cardinal. Moreover, for each cardinal, whether it is a finite cardinal or infinite cardinal, there is a greater cardinal. — TonesInDeepFreeze
The only reason something like a sequence of numbers can go on forever, is because of Infinity. It is not because the sequence of numbers are Infinite. — Philosopher19
But {0 1 2 3 ...} is not notation that for every natural number there is a greater natural number, but rather it is an informal notation to stand for the set of all and only the natural numbers. — TonesInDeepFreeze
But {0 1 2 3 ...} is not notation that for every natural number there is a greater natural number, but rather it is an informal notation to stand for the set of all and only the natural numbers. — TonesInDeepFreeze
Your posting is an absurd loop — TonesInDeepFreeze
One might argue that the latter encompasses imagining that the count to infinity is complete, but one cannot imagine such a thing. — Philosopher19
The way set theory proves there exists a set with all and only the natural numbers is by an axiom from which we prove that there exists a set with all and only the natural numbers. — TonesInDeepFreeze
Then why do you think bijection requires counting? — Banno
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