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submitted 9 months ago by [email protected] to c/[email protected]

You ever see a dog that's got its leash tangled the long way round a table leg, and it just cannot grasp what the problem is or how to fix it? It can see all the components laid out in front of it, but it's never going to make the connection.

Obviously some dog breeds are smarter than others, ditto individual dogs - but you get the concept.

Is there an equivalent for humans? What ridiculously simple concept would have aliens facetentacling as they see us stumble around and utterly fail to reason about it?

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[-] [email protected] 5 points 9 months ago* (last edited 9 months ago)

Infinity. We're simply too dumb to grasp it. Example:

3*(1/3) = 3/3 = 1
3*(1/3) = 3*(0.333...) = 0.999...
0.999... = 1

That "..." means "it continues to the infinite". And yet when you show this reasoning to people, they keep "looking" for the last 9, to claim that 0.999... is not the exact same as 1.

And that applies to all humans. You might counter it rationally, you might train yourself to recognise "it's infinite, so theoretically it'll behave in a certain way", but you don't grasp it. I don't, either.

[-] [email protected] 4 points 9 months ago

My "easier" way to think of this one:

1 - 0.999... = 0

That is, if you subtract 0.999... from 1, what is the result? It's an infinitely small value, which can only logically be expressed by 0.

[-] [email protected] 2 points 9 months ago
[-] [email protected] 2 points 9 months ago

That's exactly what it is--but when the "..." is infinitely long, you never get to the "1". There is no "1" at all.

[-] [email protected] 2 points 9 months ago* (last edited 9 months ago)

0.999… means the value of the limit of a sequence {0.9, 0.99, 0.999, …} as number of 9s (or length of a sequence) goes to infinity, and the limit is very clearly 1 in my mind.

[-] [email protected] 2 points 9 months ago

Actually infinity is easy to understand.

If you were to walk in a straight line, you would never get to the end of the earth - it is infinite.

Its finitism that is impossible to understand.


3*(1/3) = 3/3 = 1 3*(1/3) = 3*(0.333...) = 0.999... 0.999... = 1

This a problem of the number base you're using, not infinity. One third is a finite number which cannot be expressed in base 10.

[-] [email protected] 2 points 9 months ago

Why would it be the same as 1, wouldn’t it always be 0.9 unless you round up at some point.

[-] [email protected] 3 points 9 months ago

There's lots of proofs for this but this is the simplest one.

.333... = 1/3
.333... • 3 = .999...
1/3 • 3 = 1
Therefore .999... = 1

[-] [email protected] 1 points 9 months ago* (last edited 9 months ago)

Why is .333 being treated the same as a third?

You could have .3 of 2.7 and that wouldn’t be a third. So I don’t see why .3 times 3 would be anything other than 0.9?

[-] [email protected] 3 points 9 months ago

In this case you literally divide 1 by 3. And that's 0.3333 . And if you multiply 1/3 by 3 you get 1 and if you multiply 0.3333 by 3 you get 0.9999. So these two are the same.

[-] [email protected] 3 points 9 months ago

.333... Not .333

The "..." Here represents an infinitely repeating number.

In this context 1/3 = .333...

[-] [email protected] 1 points 9 months ago* (last edited 9 months ago)

Just pretend I added dots. But that still doesn’t change anything?

Imagine a pizza, I can divide that pizza into halves, thirds, quarters, etc. because conceptually they represent splitting a defined thing into chunks that are the sum of its whole. 1/3 can exist in this world of finites.

0.333… is unending. I can’t have 0.333… of a pizza, because 0.333… is a number and that makes as much sense as saying I’ll have 2.8 pizza. Do I mean 2.8 times a pizza, 2.8% of one? Etc.

[-] [email protected] 1 points 9 months ago

1/3 being equal to .333... Is incredibly basic fractional math.

Think about it this way. What is the value of 1 split into thirds expressed as a decimal?

It can't be .3 because 3 of those is only equal to .9
It also can't be .34 because three of those would be equal to 1.2

This is actually an artifact of using a base 10 number system. For instance if we instead tried representing the fraction 1/3 using base 12 we actually get 1/3=4 (subscript 12 which I can't do on my phone)

Now there are proofs you can find relating to 1/3 being equal to .333... But generally the more simplistic the problem, the more complex the proof is. You might have trouble understand them if you haven't done some advanced work in number theory.

[-] [email protected] 2 points 9 months ago

Is there a number system that's not base 10 that would be a "more perfect" representation or that would be better able/more inherently able to capture infinities? Is my question complete nonsense?

[-] [email protected] 1 points 9 months ago

Different bases would have different things they cannot represent as a decimal, but no matter what base you can find something that isn't there.

For real world use base 12 is much nicer than base 10. However it isn't perfect. Circles are 360 degrees because base 360 is even nicer yet, but probably too hard to teach multiplication tables.

[-] [email protected] 1 points 9 months ago* (last edited 9 months ago)

I get its basic shit that’s over my head. I’m just trying to understands

If the only reason is because 1/3 of 1 = 0.9, than id say the problem is with the question not the answer? Seems like 1 cannot be divided without some magical remainder amount existing

If I have 100 dogs, and I split them into thirds I’ve got 3 lots of 33 dogs and 1 dog left over. So the issue is with my original idea of splitting the dogs into thirds, because clearly I haven’t got 100% in 3 lots because 1 of them is by itself.

Likewise would 0.888… be .9? If we assume that magical remainder number ticks you up the next number wouldn’t that also hold true here as well?

And if 0.8 is the same as 0.888888888…, than why wouldn’t we say 0.7 equals 0.9, etc?

[-] [email protected] 2 points 9 months ago* (last edited 9 months ago)

I get its basic shit that’s over my head.

It's over the head of everyone. That's why I shared it here.

Likewise would 0.888… be .9?

No, but 0.899... = 0.9. This only applies to the repeating sequences of the last digit of your base. We're using base 10 so it got to be 9.

If I have 100 dogs, and I split them into thirds I’ve got 3 lots of 33 dogs and 1 dog left over. So the issue is with my original idea of splitting the dogs into thirds, because clearly I haven’t got 100% in 3 lots because 1 of them is by itself.

Then you split the leftover dog into 10 parts. Why 10? Because you use base 10. Three of those parts go to each lot of dogs... and you still have 1/10 dog left.

Then you do it again. And you have 1/100 dog left. And again, and again, infinitely.

If you take that "infinitely" into account, then you can say that each lot of dogs has exactly one third of the original amount.

[-] [email protected] 2 points 9 months ago

0.333... represents 0.3 repeating, which has an infinite number of 3s and is exactly equal to 1/3.

[-] [email protected] 4 points 9 months ago

I don't agree that they are the same.

It's just that the difference is infinitely small

[-] [email protected] 0 points 9 months ago

The difference is zero, so they’re equal.

[-] [email protected] 0 points 9 months ago

Well, you state that as a fact, but I’m going to say that the difference is infinitely small, so they are equal

[-] [email protected] 2 points 9 months ago* (last edited 9 months ago)

Because it isn't 0.9; it's 0.999... with the ellipsis saying "repeat this to the infinite" being part of the number. And you don't need to round it up to get 0.999... = 1, since the 9 keeps going on and on, so their difference is infinitesimally small = zero.

Another thing showing that they're the same number is that there is no number between them. For example:

  • 0.9 (no ellipsis) and 1 are different because 0.95 is between them
  • 0.95 and 1 are different because 0.97 is between them
  • there's no number between 0.999... (with ellipsis) and 1, so they are the same. inb4 no "last nine" because it's infinite.
[-] [email protected] 2 points 9 months ago

One way to tell if two numbers are equal is to show there’s no real number between them. Try to formulate a number that’s between 0.999… and 1. You can’t do that.

[-] [email protected] 3 points 9 months ago* (last edited 9 months ago)

But between 0.999 and 1 is 0.9999.

If something comes ever increasingly close to, but never physically touches something else, would you say it’s touching it?

[-] [email protected] 3 points 9 months ago

0.999… means infinitely repeating 9s. There’s no more 9 to add that hasn’t already been added. If you can add another 9, then it’s not infinitely repeating.

[-] [email protected] 1 points 9 months ago

So it never ends, and it stays 0.9… infinitely?

Still not a 1.

[-] [email protected] 2 points 9 months ago

It's an infinite number of nines after the decimal.

Or think of it another way. What number would you subtract from 1 to get 0.999... ? The answer is 0.

[-] [email protected] 2 points 9 months ago

let x = 0.999...

so 10x = 9.999...

subtract first line from second:

9x = 9

divide by 9

x = 1

[-] [email protected] 1 points 9 months ago

an asymptote 😎

[-] [email protected] 2 points 9 months ago* (last edited 9 months ago)

No, because that "some point" will never happen. There is no last nine to round up, because if there were a last nine, they wouldn't be infinitely many.

There are many different proofs of this online, more or less rigorous.

[-] [email protected] 1 points 9 months ago

In the real world when you see .9 you often should round it. You rarely have as much precision as presenting - .5 should generally be seen as 1 unless you have reason to believe the measurement is that precise.

[-] [email protected] 1 points 9 months ago

.333... Is a third. That's just a quirk of base 10. If you go to a different number system you won't run into that particular issue.

The most common other base people know of is binary. Base 2. So in binary the fraction would be 1/11 and then 1/11(binary)=1/3(base 10).

I remember talk back in the day that base 12 is good for most common human problems. Some people were interested in trying to get people to switch to that.
1/3 of 12 is 4.
So 4/12=1/3=3.33333.../10

.333... Is just the cursive way of writing 1/3.

I still don't "grasp" infinity. I'd recon you'd need an infinite mind to grasp infinity.

[-] [email protected] 1 points 9 months ago* (last edited 9 months ago)

1/3 of 10 is 3
3 x 3 is 9

Yet

1/3 of 1 is .3
.3 x 3 is 1?

Just does not compute for me.

[-] [email protected] 4 points 9 months ago

1/3 of 10 is 3.333...

1/3 of 1 is .333...

It's like when people come to America and are surprised when tax isn't included in sale prices. The .0333... you forgot to add on will get you in trouble with the universes math IRS.

this post was submitted on 30 Nov 2023
188 points (95.2% liked)

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