The biggest difference (other than the existence of infinity) is that the upper limit is inclusive in summation notation and exclusive in for loops. Threw me for a loop (hah) for a while.

[–] outdated_belated@lemmy.sdf.org 10 points 1 year ago (1 children)

Nah, look at the implementation above:

n <= 4

Means it’s inclusive.

You’re probably referring to some other implementation that doesn’t involve such fine control, like Python where range(4) means [0 1 2 3]

[–] radix@lemm.ee 2 points 1 year ago (1 children)

Oh yeah, I meant generally. Isn't it most common if not best practice to say for (i = 0; i < whatever; i++)?

[–] outdated_belated@lemmy.sdf.org 2 points 1 year ago

Fair. I guess to accommodate zero-indexing so that it still happens whatever times, not whatever + 1 times.

[–] affiliate@lemmy.world 1 points 1 year ago (1 children)

i thought this was pretty weird too when i found out about it. i’m not entirely sure why it’s done this way but i think it has to do with conventions on where to start indexing. most programming languages start their indexing at 0 while much of the time in math the indexing starts at 1, so i=0 to n-1 becomes i=1 to n.

[–] radix@lemm.ee 4 points 1 year ago (1 children)

My abstract math professor showed us that sometimes it's useful to count natural numbers from 1 instead of 0, like in one problem we did concerning the relation Q on A = N × N defined by (m,n)Q(p,q) iff m/n = p/q. I don't hate counting natural numbers from 1 anymore because of how commonly this sort of thing comes up in non-computer math contexts.

[–] affiliate@lemmy.world 2 points 1 year ago

yeah thats a good example and it shows weird the number 0 is compared to the positive integers. it seems like a lot of the time things are first "defined" for the positive integers and then afterwards the definition is extended to 0 in a "consistent way". for example, the idea of taking exponents a^n^ makes sense when n is a positive integer, but its not immediately clear how to define a^0^. so, we do some digging and see that a^m+n^ = a^m^a^n^ when m and n are positive integers. this observation makes defining a^0^=1 "consistent" with the definition on positive integers, since it makes a^m+n^ = a^m^a^n^ true when n=0.

i think this sort of thing makes mathematicians think of 0 as a weird index and its why they tend to prefer starting at 1, and then making 0 the index for the "weird" term when it's included (like the displacement vector in affine space or the constant term in a taylor series).