Why is 3/3 equal to 1?Ok, so 1/3 is 0.33333 forever. 2/3 is 0.6666 forever. So, if that's the case, why is 3/3=1 and not 0.99999 forever? Where does the last little bit get added to 3/3 to have it equal 1?
>>16991740Because the "last little bit" is 0infinitesimals can't exist in the standard real number systemhttps://en.wikipedia.org/wiki/Archimedean_property
>>16991740You just have to remind yourself that math isn't real.Trying to explain/measure reality with ten symbol system is a laughable act, and in essence very limiting to mankind.
>>16991740.333... tends toward 1/3, so its limit is 1/3.Just take the limit and add it up.>why is 3/3=1 and not 0.99999 forever?It's equal to both. .999... is another way of writing 1 since the limit of .999... is 1. But, yes .333... * 3 is equal to .999... and is referred to as 1, since that's where it tends toward.
>>16991740>why is 3/3=1 and not 0.99999 forever?false, it is equal to .99999...what do you even mean by 3/3 = 1? Clearly 3 = 3, 4 = 4. How do you know that 3-3 = 0? Define to us what it means to be equal.Is a crab apple equal to a fuji apple? No? But they're both apples!Is a white man equal to a black man? Yes? But white isn't the same as black!Is 16:00 equal to 4:00 PM? Yes? But how is 4 = 16?Math requires definitions of objects and relations. Equality and equivalence classes (=), order (< or >), upper or lower bounds, all of these you learn early on when you start doing math rigorously. In calculus, to find the area under a curve, you start with rectangles of well defined area, then keep adding them to fill up as many of the gaps as you can. As you continue to fill in the gaps under this curve, if you continue until the gaps get close to zero, isn't it the same as the area under a curve? What is .99999999... to you other than 9/10 + 9/100 + 9/1000 + ...? For each step we take, aren't we getting closer and closer to 1? For any arbitrary gap size, say .0001, can't I get a sum that's closer to the number 1 than that gap, say .99999? Aren't all the sums after .9999 closer to 1 by less than .0001? This is how equality is defined for these specific objects. To define clock times, you use mod arithmetic equality or equivalence classes, and similarly for even or odd numbers, (equality mod 2).Right now you should also be asking, then how do you define a number? Just take a real analysis class or read an intro book.
>>16991803Honestly, I think the problem is with us using base 10. We should use a real base system like base 10 instead.
>>16991740Why is 1/1 equal to 1? Why is 10/10 equal to 1? Why does 1 divide easily into 10 parts but not 9 parts?There's your answer.
>>16991740Both are the same.x = 0.99999910x= 9.999999Subtract9x=9x=10.999999 = 1
>nigger brained retards on /sci/ stuck on 1/3 forevertiresome
>>16991900>x = 0.999999>10x= 9.999999>Subtract>9x=9
>>16991740Because 1/3 is not exactly 0.333...; 0.333... is just the decimal way of getting infinitely close to a true third.It’s like how 3 is not exactly a third of 10, but it’s the closest whole number you can use. Since you can’t divide 10 evenly by 3, you keep adding more 3s after the decimal to get closer and closer to a true third: 0.3, then 0.33, then 0.333, and so on.So 0.333... is not really a true third like 1/3, it’s just the decimal system trying to represent something that does not have a decimal form, so you can’t really make computations with it in that form.
1/3 = 3/10 + 1/30= 0.3 + 1/30= 0.33 + 1/300= 0.333 + 1/3000:= 0.333... + 1/inf= 0.333... + 0= 0.333...
>>16991740God adds it suddenly when you get to the last number, but it's very fast
>>16991931wouldn't it be 9x=9.0000000000000000000000000 texhnically
>>16991803why this makes senseI can't accept a fact that I've spent years on literally nothing
>>16992144What's 9x9 retard
>>16992224sorry to hear that, seems you can't even use a comma.it's 81. No problem buddy. Take care.
>>16991740But maybe... maybe you found a zero day exploit in reality and until math gets patched, we can.. turn numbers into slightly smaller numbers? Like when you go to a casino and can reliably turn a pile of money into a smaller pile of money.
>>169923009x9 is the same as 9x.9, dumbfuck, no matter how many 9s you put there it will never be 9, axiomatically stating that x=.999.. and then magically turning x into 1 two lines later is a perfect example why 0.999..=1 dogmatists are braindead retards
>>16991740because [math]3 \neq 0[/math] and thus [math]3^{-1}[/math] is the multiplicative inverse of [math]3[/math] which, by definition, requires [math]3 \cdot 3^{-1} = 1[/math]
The little bit leftover approaches zero and at infinity, is zero
