you said 1/3 ≠ 0.333... which is false. it is exactly equal. there's no flaw; it's a restriction in notation that is not unique to the decimal system. there's no "conflict with reality", whatever that means. this just sounds like not being able to wrap your head around the concept. but that doesn't make it a flaw.
pyre
joined 7 months ago
is that val kilmer
wake up calls don't do shit when you're not interested in "waking up"
yeah that's because the little ones mean "hii" and the big ones mean "HELLO???!!"
nice try DoD
fair enough, but i think the confusion for that commenter comes from a misunderstanding of the definition of the mathematical concept rather than the meaning of the English word. they just think irrational numbers are those that have infinite decimal digits, which is not the definition.
not really. i get it because we use rational to mean logical, but that's not what it means here. yeah, real and normal are stupid names but rational numbers are numbers that can be represented as a ratio of two numbers. i think it's pretty good.
you're thinking about this backwards: the decimal notation isn't something that's natural, it's just a way to represent numbers that we invented. 0.333... = 1/3 because that's the way we decided to represent 1/3 in decimals. the problem here isn't that 1 cannot be divided by 3 at all, it's that 10 cannot be divided by 3 and give a whole number. and because we use the decimal system, we have to notate it using infinite repeating numbers but that doesn't change the value of 1/3 or 10/3.
different bases don't change the values either. 12 can be divided by 3 and give a whole number, so we don't need infinite digits. but both 0.333... in decimal and 0.4 in base12 are still 1/3.
there's no need to change the base. we know a third of one is a third and three thirds is one. how you notate it doesn't change this at all.
non repeating
it's literally repeating
.333... is rational.
at least we finally found your problem: you don't know what rational and irrational mean. the clue is in the name.
you have to do this now
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honestly that seems to be the only argument from the people who say it's not equal. at least you're honest about it.
by the way I'm not a mathematically adept person. I'm interested in math but i only understand the simpler things. which is fine. but i don't go around arguing with people about advanced mathematics because I personally don't get it.
the only reason I'm very confident about this issue is that you can see it's equal with middle- or high-school level math, and that's somehow still too much for people who are too confident about there being a magical, infinitely small number between 0.999... and 1.