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[an-salad]

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…(…)…

[LuckyR]

Your point ?

[Sy Borg]

I asked AI if there are an infinite number of infinities:

Yes, there are infinitely many different sizes of infinity. This comes from Georg Cantor's work on set theory, which shows that infinities can be compared by their cardinality (size). For example:
The set of natural numbers {1, 2, 3, ...} has a cardinality called aleph-null (ℵ₀), the smallest infinity.

The set of real numbers (all numbers on the number line) has a larger cardinality, often denoted as 2^ℵ₀ or the continuum.

Cantor's diagonal argument proves that for any infinite set, you can construct a larger one (e.g., its power set). This process repeats indefinitely, creating an infinite hierarchy of infinities, each larger than the last (ℵ₀, ℵ₁, ℵ₂, ...). Thus, there’s no "largest" infinity, and the number of distinct infinities is itself infinite.

However, that is just mathematics. In physics, matter is not infinitely indivisible in a practical sense. At this stage, we can divide matter into quantum wavicles but no more. Theoretically, the Planck scale (approx 1.6 x 10⁻³⁵ metres) is the smallest scale at which the concepts of size or time are meaningful. After that, the laws of physics break down.

Does reality also have an upper size limit? As far as our theories go, there is none. Odd that there's a limit to how small you can go but not a limit to how large.

[value]

Interesting topic!

The idea of ‘infinite number’ is invalid because an actual infinity cannot be counted.

Cantor's diagonal argument proves that for any infinite set, you can construct a larger one (e.g., its power set). This process repeats indefinitely

What is forgotten in the argument is that for an 'infinity' to be fulfilled, the mathematician would need to count into infinity. The mind of the mathematician - which in a philosophical argument could be replaced by the concept time - is excluded from the consideration.

It is through the mind of the mathematician, and its potential for actualization in time, that the idea of a potential infinity is possible.

An actual infinity is beginning-less of nature and cannot be applicable to a pattern such as a number.

[Sy Borg]

Yes, it's all completely theoretical because, as you say, it would take forever to count a single infinity, not to mention any containing or contained infinities.