The real number line and infinity
The real number line and infinity
If there are an infinite number of natural numbers (“points”) on the infinite number line, and an infinite number of points (fractions) in between any two of those natural numbers, and an infinite number of points (fractions) in between any two of those points/fractions, and an infinite number of fractions in between any two of those fractions/points, and…ad infinitum, then that must 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 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…(…)…
Re: The real number line and infinity
Yep...but those infinities occur between two finite points.Foshizzle wrote: ↑Wed Apr 23, 2025 9:32 am If there are an infinite number of natural numbers (“points”) on the infinite number line, and an infinite number of points (fractions) in between any two of those natural numbers, and an infinite number of points (fractions) in between any two of those points/fractions, and an infinite number of fractions in between any two of those fractions/points, and…ad infinitum, then that must 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 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…(…)…
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Impenitent
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Re: The real number line and infinity
but finite points in the day time are something else...
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MikeNovack
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Re: The real number line and infinity
Foshizzle --- If you want countable vs non-countable infinities explained, move to the "philosophy of mathematics" section of the forum and I'll try to help you understand. The way you are going about it going to prevent progress.