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

i don’t think any number system can be safe from infinite digits. there’s bound to be some number for each one that has to be represented with them. it’s not intuitive, but that’s because infinity isn’t intuitive. that doesn’t mean there’s a problem there though. also the arguments are so simple i don’t understand why anyone would insist that there has to be a difference.

for me the simplest is:

1/3 = 0.333…

so

3×0.333… = 3×1/3

0.999… = 3/3

some people are hot

definitely keep trying to make yourself feel better by reenacting the “i was merely pretending” meme

dude some of us have smaller tones ok don’t tone shame

wow, already exhausted the dialog tree huh? you looped faster than a bethesda npc

i cannot believe how openly anti-nazi some books are! we should burn these intolerant books!

AI is new, Windows has been doing it in advance for decades.

i know, that’s what i was commenting on.

when your canoe rental is really going for the SEO

idc about recalls. why is this deathtrap legally allowed on the streets?

i love how the standard went from “the appearance of impropriety” to “you know what, just leave the money on the counter”.