This goes back to an old riddle written by Lewis Carroll of all people (yes, Alice in Wonderland Lewis Carroll.)
A stick I found,
That weighed two pound.
I sawed it up one day.
In pieces eight,
Of equal weight.
How much did each piece weigh?
(Everyone says 1/4 pound, which is wrong.)In Shylock’s bargain for the flesh was found,
No mention of the blood that flowed around.
So when the stick was sawed in eight,
The sawdust lost diminished from the weight.That’s just pretentious. Oh your magic stick was exactly two pounds? The only right answer is “a little bit less than 1/4 pound”? Your stick weighted about 2 pounds, the pieces weigh about 1/4 pound. Get your wonderland shit out of here Lewis.
He had another good one too… imma have to look it up because I don’t have it memorized…
John gave his brother James a box:
About it there were many locks.
James woke and said it gave him pain;
So gave it back to John again.
The box was not with lid supplied
Yet caused two lids to open wide:
And all these locks had never a key
What kind of box, then, could it be?As curly headed Jemmy was sleeping in bed,
His brother John gave him a blow on the head.
James opened his eyelids, and spying his brother,
Doubled his fists, and gave him another.
This kind of a box then is not so rare
The lids are the eyelids, the locks are the hair.
And any schoolboy can tell you to his cost
The key to the tangles is constantly lost.Love the reasoning. Reminds me of how “1 + 1 equals 3 for suffuciently large valies of 1” is actually true when talking about physical objects, since there’s always some rounding involved.
i’ve seen a few people leave more algebraic/technical explanations so i thought i would try to give a more handwavy explanation. there are three things we need:
- the sum of two numbers doesn’t depend on how those numbers are written. (for example, 1/2 + 1/2 = 0.5 + 0.5.)
- 1/3 = 0.33…
- 1/3 + 1/3 + 1/3 = 1.
combining these three things, we get 0.99… = 0.33… + 0.33… + 0.33… = 1/3 + 1/3 + 1/3 = 1.
it’s worth mentioning the above argument could be refined into an actual proof, but it would require messing around with a formal construction of the real numbers. so it does actually explain “why” 0.99… = 1.
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.
But if the cake has 7 atoms, better get cover on a nuclear bunker just to be safe.
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.
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
If you take into account quantum fluctuations each piece will have a uniquely different mass at any given moment of time.
