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Comment by mSparks | Hacker News Reader

not checked this myself. but. my assumption is that this also applies when defining the numberline as a finite circle.

for example on a circle of circumferance 15, 14 is also equal to -1, 13 is equal to -2 etc.

which says the sum of 1+2+3... averages to -1/12

This is normally called the integers modulo N, and this is not a useful way to look at this infinite sum. One way to tell is that if you didn't already know the answer, there's no way to get it from the construction.

Nonesense. Since when did 1.2 modulo 2 equal -0.8

Er, if you're working in the reals modulo a number, then all numbers that differ by a multiple of the modulus are regarded as equal (or equivalent). So in the reals modulo 2, it is indeed the case that 1.2 is equal to -0.8.

Why do you think otherwise?

But now you've moved away from talking about the integers mod N, which is what zeroer was talking about[0] which was in response to you talking about the numbers wrapped around a circle[1]. Their response to you seemed reasonable, but I don't understand why you leaped to talking about real numbers, nor why you claim that 1.2 is not equal to -0.8 when working modulo 2.

[0] https://news.ycombinator.com/item?id=12106633

[1] https://news.ycombinator.com/item?id=12106409

because to get 0.5 for the sum of 1-1+1-1+.... requires real numbers. I never restricted it to integers.

The point of the construct is it applies to a circle of arbitrary/unknown length 14,12.2, 500,000 million billion point 6 light years.

and the average of the sum of 1+2+3+4+... will be/tend to -1/12

and its easy to test, just use a signed x bit number.

  > ... to get 0.5 for the sum of
  > 1-1+1-1+.... requires real numbers.

Actually it doesn't, it only requires the rationals.

But it's clear now that you're not really talking about maths at all, so the comment about existing, established theory about modular arithmetic doesn't really help. You seem to be doing something, well, different.

And regardless, in the long-established theory of modular arithmetic, 1.2 is equal to -0.8 mod 2, regardless of you claiming that it's nonsense.

So at this point I have no idea what you're talking about.

meh, I tend to skip thinking about the rational numbers when I move onto this hardcore theory stuff :p

There are two ways of constructing a number line from -inf to +inf

The first, is that "nothing exists" to the left of -inf or to the right of +inf The other, more useful, is that -inf=+inf+1 and +inf=-inf-1, (or -inf=+inf, never remember which is the more useful) and they form a loop. Such as that constructed by a signed integer. e.g. e.g. with an 8 bit number 127+1 = -127

This has nothing to do with modulo afaik. (but all the basic construct stuff is related) and is more to do with every dimension being curved in another (meaning they always form such loops)

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