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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 5 Oct 2024 14:44:05 -0700
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On 10/5/2024 6:32 AM, Richard Damon wrote:
> On 10/5/24 8:18 AM, WM wrote:
>> On 05.10.2024 13:12, Richard Damon wrote:
>>
>>>
>>> But actual infinity doesn't exist.
>>>
>> How can bijections between infinite sets exist then.
>>
>> Regards, WM
>>
> 
> Because the sets exist as what you think of as "potential" infinity, 
> which are actaully existing sets, we just don't need to generate the 
> full set before we use them (since that is the impossible step).
> 
> Infinte bijections take an infinite number of steps to complete 
> directly, but can be seen correct by induction.

Cantor pairing means that any pair of natural numbers can be mapped into 
a unique index and vise versa. I actually had some fun with them:

https://youtu.be/XkwgJt5bxKI


> 
> Your problem is a failed understanding of what it means to "exist"