Minimum population size given the average

I had a thought experiment that I was interested in formalising. I don’t have a maths background so apologies.

How can you calculate the possible population sizes for a given average of whole numbers?

Assuming that the number of significant digits is infinite, the population consists of whole numbers only and, for example, the average is exactly 0.9.

What I have worked out (and think is correct) is that for any population size, N, the decimal part of the output will be caused by a remainder going from 1/N to N-1/N. So the denominator of any fraction that reduces to 0.9 is in the set of possible populations and the minimum population size is therefore 10 i.e 9/10 going up to infinity

My question is how is this more formally worked out. Is there a name for all of the fractions that reduce to 0.9 or are they simply multiples of 0.9?

Are there any other tips or tricks I missed?

What spells are affected by the size of the caster?

What spells are affected by the size of the caster?

For context, I’m playing a kobold sorcerer in my D&D campaign, and have recently learned on Reddit that he cannot carry any of the medium-sized party members with Dimension Door or Thunderstep, since both spells are affected by the size of the caster:

Dimension door:

You can also bring one willing creature of your size or smaller who is carrying gear up to its carrying capacity.

Thunderstep:

You can also teleport one willing creature of your size or smaller who is carrying gear up to its carrying capacity.

Although I’m mostly interested in sorcerer spells, I’m wondering if there’s a list of all spells affected by playing a small race.

Galaxy S9 home screen folders: Can I enlarge app icon size within a folder?

I took home a new Samsung Galaxy S9 last weekend. As I usually do with new phones, I placed a bunch of my app shortcuts on the home screen, then grouped similar types of shortcuts together in “folders”. For example, the Music folder with 6 icons:example: Music folder app shortcuts

Unlike my previous phone (LG G5), these grouped shortcuts are barely legible because they’re so tiny. Is there any way to enlarge them (and thus also have less icon gridspace available per folder)?

Is the size of the entrance pupil the same as the size of the effective aperture?

I understand that the entrance pupil is the image of the aperture as seen from the front of the lens. However, is the size of the entrance pupil the same as the size of the effective aperture? In other words, if I measure the size of the entrance pupil by looking at it, will that be equivalent to the focal length of the lens divided by the f-number (with the focus set to infinity)? I know that sometimes this is hard to estimate because of the shape of the aperture blades, but I was wondering whether pupil and aperture can be quite different (perhaps at very low magnification).

Почему аннотация @Size не выводит ошибку?

Хочу попрактиковаться с валидацией бинов. Использую аннотацию @Size:

@Size(min = 22) String i; //... i = "3"; System.out.println(i); 

Минимальная длина – 22 символа, я присваиваю значение длиной 1 символ, но почему то никакой ошибки не происходит. Правильно я понимаю, что аннотация должна вывести какую то ошибку?