# Problem with infinity? [closed]

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.

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. Feb 24, 2022 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. Feb 24, 2022 at 20:21
• That's like saying that a pizza grows when it's cut in 10 parts instead of 8. Feb 24, 2022 at 20:36
• An infinty of finite parts makes an infinity whole while an infinity of infinitesimal parts makes a finite whole. Feb 25, 2022 at 18:48
• @MauroALLEGRANZA Isn't the series 1/2+1/4+1/8+...=1 'an infinity of finite parts'? Feb 27, 2022 at 15:34