So you have time to discuss math here instead
Leave it to yebellz to catch my mistake
divisible by 0 is not defined, so in above definition q should be nonzero, I believe.
Also linguistics. Iām still unsure if itās possible to grab zero stones. As surely in that case I have not grabbed.
Edit: or did I grab and miss?
I think it could be possible to āgrabā zero, but I think the custom is to grab at least one, or probably significantly more than one, to not give the appearances of grabbing too few.
For people that haphazardly grab a āhandfulā of stones without too much deliberate consideration of how many they grab, they quite possibly do have a slight bias toward even or odd, depending on the size of their hand (providing an upper bound) and some psychological tendencies about not taking too few providing a lower bound. I think that not just zero is excluded, but probably also a few other small numbers (i.e., many would be unlikely to grab 0, 1, 2, or maybe even 3 stones). If one were to statistically analyze the grabs by a particular player, one might be able to determine their individual bias. However, I think across a population of players, biases could go either way towards even or odd, and one would usually not have enough data to make a reliable guess about someoneās bias. Thus, given such uncertainty, itās usually reasonable to work with the assumption of no bias.
If one became aware that their own grabs had a bias and wished to avoid that, then an alternative procedure would be to first flip a fair coin (in private) and let that choose whether to deliberately grab an even or odd number of stones. However, one might ask a similar question about the fairness of coin flipsā¦
Of course, the entire purpose of nigiri is just to provide a way to do a fair coin flip, without flipping a coin. Since the result is determined by both playersā choices, if just at least one of them acts in a randomly independent and unbiased manner, the outcome of nigiri is like a fair coin flip. Thus, one playerās bias could be erased by the other.
Relevant go meme:
All Iām thinking is:
If you have go stones at home (or access to go stones), do nigiri N times and post the results (preferably value as well as even/odd) and we can collect some data. Also mention the type of stones, just for curiousity, whether theyāre magnetic, glass, yunzi, shell etc, doesnāt matter but will probably make sense of the range of the stones grabbed. (Iād say size as well but the effort of remembering which you bought or actually measuring, especially units being a hassle).
180 each time?
My kids do this too. There is something in human nature about more is better I guess
So can we say that 0 is the least prime number?
If you can do that thatād be interesting.
It would also have to be from one attempt at a grab from whatever container they happen to be in
I guess it depends how strong the magnets are. Iāve never actually played with a magnetic set. I just imagine that all the stones stick together all the time.
Iām not a mathematician, but I would say
Dividing a positive number by 0 gives +infinity.
Dividing a negative number by 0 gives -infinity.
Dividing 0 by 0 does not have a unique solution.
In fact any finite number would be a solution of x = 0 / 0 <=> 0 = x * 0. So 0 / 0 is undefined (not-a- number or NaN according to computers).
You expect me to reveal my weaknessā¦
Still some randomness with how many stones one has lost over the years (children will readily help with that)ā¦
Okay, hereās my data:
10, 8, 7, 8, 8, 9, 12, 6, 7, 6, 7, 9, 9, 6, 8,
8, 13, 8, 8, 9, 6, 11, 8, 6, 9, 11, 11, 7, 6,
6, 7, 13, 8, 7, 7, 8, 6, 7, 9, 9, 5, 7, 5, 6,
7, 7, 6, 9, 6, 8, 8, 8, 7, 10, 6, 6, 8, 6, 11
Note: this is with magnetic stones for a medium-sized portable go board. I think the magnets may have an impact with some stones being stuck together in pairs.
I mean you can play the same game with
2/0=+infinity=1/0
=> 2=1
One probably shouldnāt expect all the usual rules for addition and multiplication to hold when one is trying to define division by zero.
For example with the complex numbers, one can define division by zero Riemann sphere - Wikipedia but still some expressions are just left undefined like ā ā ā and 0 Ć ā and 0/0 and ā/ā.
I might do this a little later myself with some glass ones and some shell ones to compare. I also have some really tiny plastic ones that came with a set that I could for funsies.
https://www.amazon.co.uk/GO-Pack-Matthew-Macfadyen/dp/1780974248
Iām not sure Iāll do it ~60 times per type though
I donāt know what is your reasoning here. Prime numbers are positive integers that are divisible by only themself and 1. Since 0 is divisible by all non-zero integers, doesnāt that make 0 the least prime number?
Yes. You canāt divide 0 by 0 (i.e. the operation 0/0 doesnāt make sense), but ā0 divides 0ā is true by the mathematical definition.
Prime numbers are only divided by themselves (and 1), so primes have very few divisors.
You said that every integer divides 0. Doesnāt that imply that 0 has infinite divisors (and it thus the least prime integer)?
You are right in some sense. The set N = {0,1,2,ā¦} endowed with the divisibility relation is a partially ordered set. The smallest element is 1. Then come the prime numbers. And 0 is the largest element.
Prime numbers are positive integers
Doesnāt zero already fail this first step. Is it an integer? Is it positive? And thatās before you get onto the dividing business.
- Positive
- Negative
- Integer
- Hero
0 is not prime and I tried to make clear that it more not-prime than any other integer.