Medicine parties are the best. They know life is short.
1 Like
How is this even debated? There’s proofs that really are not hard to understand. I don’t know how you can dispute a proof, but then again, people believe geometry is fake and the earth is flat 
I think it’s legitimately confusing because there’s a single number with two different decimal representations. It’s a flaw (apparently unavoidable) of decimal representation, but the “simple” answer is that 0.999… shouldn’t be a valid number. To make it worse, most normal people think of decimals as the ground-truth numbers (your paycheck is written in decimal!), and fractions as the weird mathematical trick. So proving that 1 and 0.999… both correspond to the same rational is less convincing.
What do you mean by “valid” number? It is a number, it is valid, it’s just irrational (in the mathematical definition)
0.9 recurring is both perfectly valid and rational. It is rational because it equals 1. However, if you think it’s irrational because it doesn’t terminate, that is also incorrect. 0.3 recurring is rational and it equals 1/3. In fact, all decimal representations that terminate or repeat infinitely represent rational numbers.
Oh yea duh herp derp
Got some concepts confused in my head, been a while since i studied number theory
I mean decimal representation would be clearer if the rational 1 was canonically represented as “1” in decimal notation, and 0.999… was an invalid way of writing it. Similar to how 2 / 2 is an improper representation of 1 and 6 / 4 is an improper representation of 3 / 2.
Parsing it as singular makes it sound like a mass noun. “I have zero pineapple” is appropriate with like, pulped pineapple as an ingredient. Very different from having zero pineapples, which means you don’t have any literal pineapples.
An interesting situation can also arise with power towers, for example:
=2
=2
etc.
The tower can contain any finite number of sqrt(2)'s and it will always equal 2 (evaluating from the top down, each sqrt(2)^2 reduces to 2).
In some sense, these are all alternative ways of writing the number 2.