what 1/3 of something can totally exist
what 1/3 of something can totally exist
a third of something can exist. 1/3 cannot. Get it. 1 divided by 3. 1 over 3. 1 dividido por 3.
A third of something can exist, it just can't be expressed in base 10. You can express it in any base number system that's a multiple of three.
For example, base 3 (0, 1, 2 - each place represents another power of three, so 111 in base three represents:
1(3^0) + 1(3^1) + 1(3^2) =
1(1) + 1(3) + 1(9) =
1 + 3 + 9 = 13
You can represent 1/3 exactly in base three, really easily. It's simply 0.1. This is because a decimal point symbolises the point where numbers go into negative powers, making 0.1 in base 3 equivalent to:
0(3^0) + 1(3^-1) =
0(3) + 1(1/3) =
0 + 1/3 =
1/3
I tried to simplify that for people who haven't done mathematics classes, but I dunno how successful I've been. Basically, a third of something can exist in exactly the same way as a tenth of something can; it's just that the number system we use (denary, or base 10) can't express it. If you ask me, duodecimal (base 12) is a far better system, because it allows you to express numbers divided by 1,2,3,4,6, and any multiples of those numbers. The only one you can't express correctly with it is a multiple of 5.
You could solve that problem by switching to base-60, but that might be a bit complex for most people...
Originally Posted by Fenn
Then it wouldn't be represented as .3333, therefore .9999 still wouldn't equal 1.
Cyp. You're wrong. You're literally trying to make 1 not equal 1. How a number is represented is unrelated to that number's value.
Stop being so arrogant. Just because you don't understand it, it doesn't make it untrue.
Originally Posted by Fenn
Bark at the moon.
Your conjecture states that because 1 divided by 3 is commonly understood as .3333, multiplying it again by 3 proves that .999 is equal to 1. I'm saying in .3333 in any form still does not represent an exact third. It's shorthand. Suggesting that a third can be represented in a different base still does not prove your conjecture that .3333 = 1/3rd and therefore .999 = 1/1. .1 in base 3 =/= .3333 in base 10, it equals 1/3rd. The accepted truth is that .9999 = 1 because of the absence of a number small enough to constitute the difference. I'm just saying your particular approach to proving it does not work on that level.
If you just said the lack of real infinitesimals disallows for a difference between .999... and 1, yeah I would have agreed. But even then it's not a proof of equivalence so much as it is an inability to calculate the difference mathematically.
Cype, here's a list of formal proofs by mathematicians.
Please read them.
Originally Posted by Fenn
Yeah I've read all of those. It's pretty much agreed on that .999... is smaller than one by an infinitely tiny amount, which is why it's taken as 1 in all practical application. Lack of real infinitesimals.
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