Problem with infinity?

Question

Note: See PART 2 for a better question.

1 kg of matter has infinite number of parts. Infinite number of things together can make an infinite amount of matter. 1 kg is not equal to infinite amount. We face an illogical result.

Note I: The terms 'infinite divisibility' and 'infinitesimal' MAY be related.

In logical explanations, what is the mistake in this argument?

PART 2

Does 1/2+1/4+1/8+1/16+... get over 1? First, we may (wrongly) think that the answer is 'Yes', but actually the answer is 'No'.

A more interesting form of this problem: An amount starts from 0, and increase by every moment. Does it eventually get over 5?

This is the best example of possible mistake of intuition that I faced (I have not examined all examples), and I call it a paradox:

For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. - Series (mathematics), Wikipedia

Note II: 'Zeno's paradoxes' and 'Convergent series' may be related.

A possible answer?

I think the answer to both questions may be that 'there is an infinite number of numbers or measurements between 0 and a finite number'.

There are not an infinite number of parts in 1kg of matter for one thing. — DJClayworth, Feb 24 '22 at 19:24
"Infinite number of things together can make an infinite amount of matter" is false: 1/2 + 1/4 + 1/8 + ... = 1, make it kilograms. — Conifold, Feb 24 '22 at 20:21
That's like saying that a pizza grows when it's cut in 10 parts instead of 8. — RodolfoAP, Feb 24 '22 at 20:36
An infinty of finite parts makes an infinity whole while an infinity of infinitesimal parts makes a finite whole. — Mauro ALLEGRANZA, Feb 25 '22 at 18:48
@MauroALLEGRANZA Isn't the series 1/2+1/4+1/8+...=1 'an infinity of finite parts'? — Koorosh, Feb 27 '22 at 15:34
FWIW, I suggest reading an introductory book in Real Analysis. Stepehen Abott's "Understanding Analysis" may be a good starting point. — Agnishom Chattopadhyay, Apr 22 '22 at 15:26

score 4 · Answer 1 · answered Feb 24 '22 at 20:38

The fact that "an infinite number of things together can make an infinite amount of matter" does not suggest that "an infinite number of things together cannot make a finite amount of matter. The first statement is not a logical implication, having an infinite number of things does not imply an infinite amount of matter.

If I have 10 things, they can have 10 kg of mass. If I have 10 things, they can also have a different amount of mass. If I have infinite things, they can have infinite mass. If I have infinite things, they can also have non-infinite mass. There is no contradiction here.

Problem with infinity?

PART 2

A possible answer?

1 Answers1

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