🧵 Untitled Thread
Anonymous at Sat, 26 Oct 2024 00:38:02 UTC No. 16449795
If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two fractions, does that mean that there are not only infinite infinities, but an infinite number of those infinities? And an infinite number of those infinities? And an infinite number of those infinities? And…(infinitely times. And that infinitely times. And that infinitely times. And that infinitely times. And…) continues forever. And that continues forever. And that continues forever. And that continues forever. And that continues forever. And…(…)…
How do you define the natural numbers without infinity?
Anonymous at Sat, 26 Oct 2024 00:55:03 UTC No. 16449825
Anonymous at Sat, 26 Oct 2024 00:57:19 UTC No. 16449830
>>16449795
through the experience of the observer
https://www.youtube.com/watch?v=b00
Anonymous at Sat, 26 Oct 2024 02:36:25 UTC No. 16449960
>>16449795
>How do you define the natural numbers without infinity?
I think you're looking at this the wrong way. It makes more sense to ask,
>How do you define infinity without the natural numbers?
since natural numbers are where we start.
Anonymous at Sat, 26 Oct 2024 10:24:53 UTC No. 16450286
>>16449960
Care to elaborate?
Anonymous at Sat, 26 Oct 2024 14:57:52 UTC No. 16450679
>>16450286
The natural numbers are called "natural" because they arise from humans counting "how many things are there?"
So in that sense, you don't need any mathematical constructs to define it, rather it becomes the base to define mathematical constructs. There is a reason that most analysis textbooks *begin* with the natural numbers, and eventually arrive at a concept of infinity.
Anonymous at Sat, 26 Oct 2024 15:15:29 UTC No. 16450705
>>16449825
0 isn't in the proper set of natural numbers