>>16920526
It’s a failure of numerical systems, .33333 = 1/3. It’s because 1/3 can’t be expressed in decimal format that we need it in the first place. Numbers are only useful as much as they can describe reality, and we have different numerical concepts to describe different phenomena. There’s no rhyme or reason for it, and you won’t be able to find one.

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You can divide 3 by 3 just once, therefore 1

Are you retarded, OP?

>>16920526
It doesn't.

You're talking about two different systems of notation, i.e., two different dialects of the same language that have different syntax and rules.

Decimal notation is the expansion of the rational term. The notation itself is a limited format, it is so precise that it generates an infinite repeating sequence that you are using your intuition to "summarize" and assume is equal to 1/3. That is called "taking the limit" of a sequence that demonstrates "convergence". In this case, the sequence converges on a number that cannot be represented in decimal notation, so you must use a different kind of notation to represent it.

This happens constantly, everywhere in mathematics. Set theory has to be translated into category theory and the notation is not the same. Algebraic geometry is not the same as the algebra you learned in high school, and so forth.

You are incorrectly assuming that the two numbers are using the same notation and mean the same thing. They do not mean the same thing. There is no "last little bit" that gets "added to 3/3". Instead, you translate French into English. 0.333333~ in decimal notation, translated into the notation used for rational numbers, making it "equivalent" (which is not at all the same thing as "equal").

>>16920532
Thanks for explaining it more thoroughly.

>>16920526
>Ok, so 1/3 is 0.33333 forever
did your rabbi tell you this?

>>16920526
>Where does the last little bit get added
There's a little 1/3 at the end of each 0.333... that gets omitted for brevity.

>>16920526
Take an intro to calculus class, buddy. Or read any intro book, there's too many out there cause it's an easy but important subject for science+math.

Start with a whole cake. Eat half the cake. Eat half of what remains. Eat half of what remains. Continue ad infinitum. Don't you basically eat the whole cake? Start with a whole cake, 1. Eat 9/10 of it, eat 9/10 of what remains, continue ad infinitum. Don't you eat all of 1?
.9999999999... -> 1
.00000000000...1 -> 0
You want to find the area of a circle. Fill it with a 3-polygon (triangle). What's the area? Now do a 4-polygon (square) instead. Now a 5-polygon instead. Continue ad infinitum. Don't you basically get the whole circle?
(n*sin(2pi/n)/2)r^2 -> pi*r^2

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0.30000....
+
0.30000....
+
0.30000....
=
0.90000....
Carry the 0.10000 through the Douval-Morrison chiral coherence splitter using the Uldermann ruleset applied to a tilted open X split set exchange, double check logic rule...and
DONE

>>16920551
0.333... has no end
Inf has no end, it's in the definition.

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>>16920564
>cake analogy

Oh, I get it now!
The 0.000...001 remains on the knife.

1/3 + 1/3 + 1/3 = (1+1+1)/3 = 3/3

3/3 = 1

But also, 1/3 = 0.333...

Therefore 0.333... + 0.333... + 0.333... = 1

>>16920526
1 is equal to .999999... forever.

1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

>>16920526
Because its not base 10

>>16920526
If you don't believe 0.999... is 1 then you also don't believe 0.333... is 1/3. There's nothing more plausible or implausible about the second case.

>>16920526
x = 0,99999999999...
10x = 9,99999999999...
10x - x = 9,999999999... - 0,9999999...
9x = 9
x = 1

>>16922065
This, the only 'mystery' is being able to represent a fraction as an infinite series.

>>16920526
Use base 60 and you won't have repeating decimals for 1/3rd.

>>16920526
Infinite series.
It's like saying :
The length of the circle is Pi.
Pi is an infinite never ending number 3,14159265358979...
Then if it never ends, then the circle never closes in itself.

let k = 1/3

3k = 1

no decimals