Under what conditions does 1/X create an infinite decimal?

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Under what conditions does 1/X create an infinite decimal?

Postby Flannel Jesus » Thu Jun 02, 2022 6:33 pm

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.
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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Thu Jun 02, 2022 7:27 pm

Flannel.

To be perfectly honest. That could give me the field medal in math.

I don’t give a shit.

I’m here to fix existence.

And before you deify me... I’m just a person like all of you.

I literally have an infinite number of infinite heavens that I’m responsible for.

I hate this world.

I even hate winning these debates.

Numbers are not what you think they are.

Language is not what you think it is.

I’m just passing through.

Don’t worry about it.
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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Fri Jun 03, 2022 7:35 am

Ecmandu wrote:Flannel.

To be perfectly honest. That could give me the field medal in math.

I don’t give a shit.

I’m here to fix existence.

And before you deify me... I’m just a person like all of you.

I literally have an infinite number of infinite heavens that I’m responsible for.

I hate this world.

I even hate winning these debates.

Numbers are not what you think they are.

Language is not what you think it is.

I’m just passing through.

Don’t worry about it.


I’ll add to this.

I don’t want your approval and I don’t want your hatred.

It’s actually an embarrassment for me to be in a world like this.

Even just to type that sentence... I just murdered a billion innocent bacteria who weren’t even trying to hurt me and have lives as valuable as mine:

I hate this world.

I even hate winning debates.

I hope the board can understand that I’m back in my body now.

I had to do a soul split to figure out why an infinite number of beings eternal heavens were corrupted.

I had no choice.

It’s extremely dangerous.

This is not the same thing as having multiple personalities.
The purpose of life is to give everyone individually what they always want at the expense of no being - forever.

The biggest problem of life is the, “hey, I don’t want this to be happening” problem for everyone.

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Re: Under what conditions does 1/X create an infinite decima

Postby Flannel Jesus » Fri Jun 03, 2022 7:48 am

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.
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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Fri Jun 03, 2022 7:52 am

Flannel Jesus wrote: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.


Ok flannel. What do you want to know about numbers and language?

I guarantee you it’s all useless.

Ask me a specific question.

One or two sentences. I’m making you work.
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Re: Under what conditions does 1/X create an infinite decima

Postby Flannel Jesus » Fri Jun 03, 2022 8:43 am

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.
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Re: Under what conditions does 1/X create an infinite decima

Postby Dan~ » Fri Jun 03, 2022 10:08 am

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.
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Re: Under what conditions does 1/X create an infinite decima

Postby Flannel Jesus » Fri Jun 03, 2022 10:14 am

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.
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Re: Under what conditions does 1/X create an infinite decima

Postby Flannel Jesus » Fri Jun 03, 2022 10:40 am

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.
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Re: Under what conditions does 1/X create an infinite decima

Postby obsrvr524 » Fri Jun 03, 2022 12:44 pm

Flannel Jesus wrote:I don't think anybody knows for sure yet if space is infinitely divisible,

Someone knows for sure that it is.

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. :D
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Re: Under what conditions does 1/X create an infinite decima

Postby Flannel Jesus » Fri Jun 03, 2022 1:01 pm

> I did discover how to divide any arbitrary angle into precisely 3 EQUAL PARTS using only straight edge and compass

Really? You should make a thread about it, this is probably bordering on Nobel prize worthy.
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Re: Under what conditions does 1/X create an infinite decima

Postby obsrvr524 » Fri Jun 03, 2022 1:13 pm

Flannel Jesus wrote:> I did discover how to divide any arbitrary angle into precisely 3 EQUAL PARTS using only straight edge and compass

Really? You should make a thread about it, this is probably bordering on Nobel prize worthy.

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).
              You have been observed.
    Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
    It's just the same Satanism as always -
    • separate the bottom from the top,
    • the left from the right,
    • the light from the dark, and
    • blame each for the sins of the other
    • - until they beg you to take charge.
    • -- but "you" have been observed --

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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Fri Jun 03, 2022 3:09 pm

Obsrvr.

With ideal forms, a 4 inch circumference circle is equal to a square with one inch on each side.

The actual mathematical “problem” is with a physical square and physical circle.

Take a 4 inch string and make a circle...

Then make a square.

Each side of the square will be less than one inch.

That’s because the corners bend.

To square a circle in physical reality, you have to add the length diagonally of the corners to the perimeter of the square.
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The biggest problem of life is the, “hey, I don’t want this to be happening” problem for everyone.

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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Fri Jun 03, 2022 3:33 pm

Flannel Jesus wrote: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.


Ether can’t be divided. That is the smallest scale and it’s infinite in scope. It’s the pure energy that makes existence a perpetual motion machine.

There’s not enough energy in existence to divide ether because it’s all the energy. It’s not a particle.
The purpose of life is to give everyone individually what they always want at the expense of no being - forever.

The biggest problem of life is the, “hey, I don’t want this to be happening” problem for everyone.

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Re: Under what conditions does 1/X create an infinite decima

Postby Ichthus77 » Fri Jun 03, 2022 3:56 pm

Somebody needs to update your software or explain to me why ec/meno & others are still talking about ether & misspelling lose/loose.

And don’t try to say it illustrates that differing norms means there’s no true norm.

We can’t know we’re wrong unless we know what right is.

The closer you are to right, the more stuff breaks down when you get it wrong.

In nature (which is also super), socially (which is in nature, which is also super), or otherwise (bringing our own level of super within the super).

You’re either in alignment or you get burned up in the testing.

Don’t be a crash test dummy :p

Ok so we’re all crash test dummies.

What was the question?

Oh… conceptual versus actual division. Think Planck & calabi yau. Maybe. Brian Greene’s Fabric.
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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Fri Jun 03, 2022 4:01 pm

Ichthus.

Ether is the ground you call god.

Omnipresent and indivisible.

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.

How much do you want to know?

Just ask.
The purpose of life is to give everyone individually what they always want at the expense of no being - forever.

The biggest problem of life is the, “hey, I don’t want this to be happening” problem for everyone.

Welcome to thinking.
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Re: Under what conditions does 1/X create an infinite decima

Postby Ichthus77 » Fri Jun 03, 2022 4:05 pm

I wish Archimedes was here.
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
- A marriage of Sartre & Levinas

“ Gloria Dei est vivens homo. “
Trans.: The glory of God is man fully alive.
- Irenaeus
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Re: Under what conditions does 1/X create an infinite decima

Postby Ecmandu » Fri Jun 03, 2022 4:06 pm

Ichthus77 wrote:I wish Archimedes was here.


Nobody ever dies Ichthus.
The purpose of life is to give everyone individually what they always want at the expense of no being - forever.

The biggest problem of life is the, “hey, I don’t want this to be happening” problem for everyone.

Welcome to thinking.
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Re: Under what conditions does 1/X create an infinite decima

Postby Ichthus77 » Fri Jun 03, 2022 4:08 pm

Don’t look at me like I’m gonna summon him. Want some caramel apples? Jk.
Fall semester ends 12/16/22. Apologies if I do not reply immediately.

“In choosing myself, I choose the other.”
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“ Gloria Dei est vivens homo. “
Trans.: The glory of God is man fully alive.
- Irenaeus
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