killing raven sun wrote: ↑Sat Jan 05, 2019 6:48 am

jliat wrote: ↑Sat Jan 05, 2019 6:24 am

killing raven sun wrote: ↑Sat Jan 05, 2019 6:18 am

, i started at "an infinite whole number",

Subtracted 1 and got a finite whole number 1 less than an infinite whole number.... (how on earth you can get to an an infinite whole number - not withstanding.. )

no, you are still thinking infinity is a value, its not, you can continue to count into infinity in a set of whole numbers that is missing "13" but the set itself is not infinite, by definitiion it lacks an element, therefore not infinite

i see you are a fan of cantor, thats your problem

Well Cantor invented set theory, which is quite foundational, and you are talking about sets... for starters, there are many types of sets, you conflate the set of whole numbers - which is infinite, with the set of whole numbers less 13, which is also infinite, though not the 'complete' set of all whole numbers. Likewise the set of primes is infinite, as is the set of primes which are odd. Though the latter is not complete.

In short "complete" all the items characteristic of a set, does not entail infinity. A set of playing cards for instance, finite and complete, or finite and missing a card.

The set of whole numbers starting at Googolplex is not complete but still infinite, and of the same size as any other Alef zero set.

And yes infinity isnt a value, so how can you count down from it! (Though it is countable by bijection)

So by definition the number of rooms in a Hilbert Hotel missing 13 has not the complete set of integers yet is still infinite. As is a Hotel with just even numbered rooms... You even said yourself the set of even or odd numbers is infinite.

Youve also missed out zero and negative numbers... "whole numbers"

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