In another thread, Ecmandu put forward a theory that I’m not sure I understand, so I won’t try to paraphrase it as I’ll undoubtedly get it wrong, but I was thinking about the problem independently myself and I think my theory has a good chance of being close to the truth, if not the literal entire truth. I’ll walk you through my thought process before I get to my conclusion.
First, I noticed that 1/3 was an infinite decimal in base 10, but it was finite in base 9 and 3. So my very first instinctual thought is, 1/X is a finite decimal if the base we’re in, B, is a multiple of X.
But then I thought to the example of 1/4 in base 10, which isn’t infinite. But 10 isn’t a multiple of 4, so what could it be?
4’s prime factors are 2 * 2. 10’s prime factors are 2 * 5. I’m pretty sure this is the key.
Here’s my theory: for 1/X in base B, if you take the unique prime factors of both X and B (so in the case of 4, we just include 2 once – the second one isn’t unique), if X has any unique prime factors that aren’t also prime factors of B, then 1/X will be an infinite decimal. If all of X’s unique prime factors are also prime factors of B, then 1/X will be a terminating, finite decimal.
Mate, if you don’t want to talk about the topic of the thread you don’t have to post. I’m not offering approval, I’m not offering hatred. If you have a constant state of embarrassment from just being alive, please for your own sake get help.
I don’t make this thread for you to make me work. I have enough work to do when I go to my actual job.
You posted a theory about infinite decimals in another thread. I posted what I think is a simpler and more correct theory here. If you don’t want to talk about it, you don’t have to.
You’re being weird though, I have no clue what the fuck you’re talking about in here.
I heard that in real life,
space is not infinitely divisible.
That means that in real life,
1/3 = 0.333333333333333330
infinitely repeating numbers only exist in a calculator.
In real life there are no infinitely repeating fractions.
I don’t think anybody knows for sure yet if space is infinitely divisible, but if that were the case (that it isn’t continuous, infinitely divisible) then at the smallest scale, there wouldn’t be any fractions at all - at the smallest scale everything would be an integer.
But, even if we took your logic at face value, you’d have to make some very interesting arguments to prove that 1/3 is impossible but 1/4 isn’t.
We only call 1/3 an infinitely repeating decimal and not 1/4 because we happen to use base 10, so we would need a reason to suppose reality cares in particular about base 10 to accept 1/4 and not 1/3. I don’t have any reason to suppose that.
The subject of what conditions are required requires too much research for me. I have an interest in why pi has its properties (because of the squaring the circle challenge that I haven’t given up on – yet) but the rest of maths complications are not of enough interest – although I did discover how to divide any arbitrary angle into precisely 3 EQUAL PARTS using only straight edge and compass - base_10 long division wasn’t required - so it worked.
The only reason I pursued it was that at one point months ago - I thought it would help me square the circle - but once I finally worked out exactly how to get that divided (about 3 months later) - I forgot how it was supposed to help.
Finding that did help with one concern - I am more assured that authoritarian claims that something is mathematically impossible (supposedly proven to be impossible long ago by some obscure genius) - doesn’t mean that it really is. I read a number of articles concerning why dividing an angel is impossible - all of which used flawed logic.
Although it is pretty simple once you know how (even embarrassingly obvious) - I don’t want to advertise it until I’m sure how it can help with squaring the circle (my real aim).
The only thing that makes form is that infinity equals motion. When it’s itself, it never becomes itself, because it never stops. That’s what creates the world of forms and identities.
