How do repeating numbers exist?

>1/3 is actually something that can exists
prove it

If you accept that 1/3 can exist you implicitly accept that 0.3333 repeating exists because they are the same thing. If you have two dollars in your wallet, then you could also say that you have the square root of 2 dollars.

*square root of 4

If I have 9 dollars, and take 6 dollars out, does that mean I have .33333...... of my dollars left?

If something is 33 years old, then 11 years is objectively 1/3 of their life.

yes.
If we used base 9, you'd have 0.3 of your original dollars. If we used base 8 you'd have 0.2666... of your original dollars. If we used base 12 you'd have 0.4 of your original dollars.

The problem is exactly that the decimal representation cannot exist, as you mentioned. There is of course a finite set of numbers/things that can be represented given a specific number of places and a certain base. And within a base, there are items that cannot be wholly expressed, like the 1/3 & 0.333... example you give. So we just use either the ellipsis or the repetition bar over the digit as a way to extend our number system, as another way to write (for example) 1/3.

Of course the number/concept exists. Our method of understanding communicating numbers as humans just isn't suited to handle it well in decimal form.

What's the problem?

how can you know that a year is a well-defined and exact quantity? (pro-tip: it's not)

REALLY ACTIVATES THE ALMONDS

1/2 = .500000000000>...

If you think that's bad then wait until you learn about pi.

>toplel

>not being part of the woke e master race

>It's not .3333....

.3333.... = 0.1 in base 3

>b-but dividing by 3 is wrong
Why is dividing by 10 right then? Because monkey fingers?

Define real

Why aren't irrational numbers real instead of imaginary if they don't exist?

there is standard year and standard day

Tell me, is .333 infinite or is it infinitesimal? I can never remember which it is.

This is like saying a word that does not have a translation in another language doesn't exist.

But zero doesn't even exist. You can't have 0 of anything.

They don't, it's just a weakness of our number system so we use 1/3 instead.

0.3 = 0.33 = 0.333 etc etc

the number of 3's you want is just for personal preference

OP, you need to realize something. Something most "I LUV SCYENCEE!" type brainlets never get. There is not a one-to-one correspondence between the real world and mathematics. Stop thinking everything in mathematics should have a "perfect" real world analogy. Mathematics is mathematics. Mathematicians do mathematics. They make definitions, and usually, out of convinience, they define their shit so that when it is applied to the real world, it makes sense. Take metric spaces as an example. en.wikipedia.org/wiki/Metric_space#Definition They didn't have to define it like it did, but they dun did it. Euclidean n-spaces with the Euclidean metric are "consequences" of these definitions, and we find analogies for them in real life. That doesn't have to be the case, though. 1+2+3+.. = -1/12 is perfectly valid MATHEMATICS, in certain systems, but it has no real world analogy, and it never will. This is also true the other way. Mathematics doesn't describe reality perfectly. Mathematics/Physics are merely models (damn fucking good models, of course) of the real world.

Are actually the two best answers in this thread. No idea what the fuck the others are trying to convince you of.

0.333333... is the result of dividing 1 by three in base 10.

Another way to write 1 divided by 3 is 1/3

Therefore 1/3 = 0.3333...

that's like saying 1/3 exists because it's defined as 1/3 of a thing. how many atoms decay over the course of a year, how many meters/planck lengths or whatever does the earth cover precisely within a year? how many smallest quantities of time pass?

This.
3.14... is bullshit. It's just 22/7

pi ~ 3 most of the time

You can define irrationals using Dedekind cuts

1/5 is 0.00110011... in binary
1/2 is 0.11111111... in ternary
OP is a retard in decimal

I have 0 dollars rn

I have had 0 gfs in my life. I'm telling you, 0 is real as fuck.

>1+2+3+.. = -1/12 is perfectly valid MATHEMATICS, in certain systems, but it has no real world analogy, and it never will.
en.m.wikipedia.org/wiki/Casimir_effect#Derivation_of_Casimir_effect_assuming_zeta-regularization

.3bar is not a number. .33bar is. You can't repeat a single digit in the decimal place. It has to be a minimum of 2 digits for the next digit to be a detected sequence, therefore predictable.

So that explains why I got shouted at when I used the bar in middle school. I never knew if using it was ever the right or wrong thing to do so I just never used it

the bible gives dimensions for a well whose circumference is exactly thrice its diameter

any observation that shows pi as something other than 3.00000000 is actually satan decieving you and throwing off your measurements to separate you from the holy word of G-d

I make them exists with these dubs

>This is also true the other way. Mathematics doesn't describe reality perfectly. Mathematics/Physics are merely models (damn fucking good models, of course) of the real world.

Because physics don't change to better suit writing things in base 10
God, some of you are idiots

this

Include me in the screencap so reddit knows I supported the best answer in this thread.

they're all based on the en.wikipedia.org/wiki/Caesium_standard