The main piece is what I’m calling all cakes that are not whole from now on
Edit - this got me thinking, once you’ve cut the first 0.333 piece and then you split the rest of the main piece in 2, who is the next side piece and who continues to hold the title of the main piece?
Yes. The knife is clean if we are cutting exact thirds. As one other user mentioned, base-10 doesn’t allow prime fractions to be conveyed cleanly, so we use repeating decimals to imply that it is a fraction.
It’s not even really a flaw. Just a property. In some sense we’ve lost the property of uniqueness of decimal representations of numbers that we had with other sets of numbers like integers. In another sense we gain alternate representations for our numbers that may be preferrable (for example 1=1.000… but also 1=0.999…).
Flaw is a bit harsh. Periodic, infinite decimals happen because the denominator is not a multiple of the prime factors of the base and thus will exist in any base.
The fun thing is this is just a consequence of how we write numbers. If you used base 12 1/3 would be 0.4. Obviously 0.4 + 0.4 + 0.4 in base 12 is 1.0, so 3 x 0.4 = 1
What’s even more fun is that things like 1/5 or 1/10 are recurring decimals in base 12.
You probably think you’ll never feel bad for saying that, but one of these nights, staying up late, thinking about the things you said and done, you’ll.
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