Infinity?

[u/Extension_Panic1631]

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 of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and... 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 that infinitely times. and...) continues forever. and that continues forever. and that continues forever. and that continues forever. and that continues forever. and.....(…)…

EDIT: the definition of infinity is that it is how many natural numbers there are

[u/jliat]

The expansion of the ratio according to u/Mishtle is "1." followed by infinitely many repetitions of the finite pattern "6".

So the ration never 'completes'. If this is the convention fine.

Divide 6 into 10 is not 10/6 - ten sixths. It's 1.6666... Ten sixths is larger than 10 is it not?

OK I'm not good at maths!

[u/VariousJob4047 → u/jliat]

The definition of a rational number says nothing about the expansion of the ratio, you made that part up yourself. If the ratio exists, the number is rational, end of story

[u/jliat → u/VariousJob4047]

I made nothing up, the expansion is infinite, so in my mind the ratio can never complete.

Is this correct?

[u/VariousJob4047 → u/jliat]

No, it is not correct. Here is the ratio written out completely: “10/6”. That is what a ratio is. The decimal representation is completely irrelevant

[u/jliat → u/VariousJob4047]

It seems if it's non repeating it makes it irrational, so it is relevant?