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this post was submitted on 17 Jul 2023
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One of the pieces is actually 0.33333....4
If you cut perfectly, which is impossible because you won't count or split atoms (and there is a smallest possible indivisible size). Each slice is a repeating decimal 0.333... or in other words infinitely many 3s. (i don't know math well that's just what i remember from somewhere)
If the number of atoms is a multiple of 3, then you can split it perfectly.
For example say there’s 6 atoms in a cake, and there’s 3 people that want cake. Each person gets 2 atoms which is one third of the cake.
The main problem is simply that math is "perfect" and reality isn't. Since math is an abstract description of causality while reality doesn't/can't really "do" infinity.
But if you really wanted to, you could bake a cake in a lab with a predetermined number of atoms and then split that cake into 3 perfect slices. However, once you start counting multiples(like atoms in a cake) you would no longer get 1/3 or 0.3 because you are now dividing a number bigger than 1(the number of atoms) so you would't get a fraction(0.3) You would get a whole number.
But if the cake has 7 atoms, better get cover on a nuclear bunker just to be safe.
Technically no
0.3333.... repeats infinitely. The 0.333...4 is not an infinitely repeating number. And since 0.333... is, there's no room to add that 4 anywhere
Which is why adding them up you get 0.999..... which is exactly and completely equal to 1