Number Theory

[Anonymous No.5694781]

1/1 = 0.99.. or 0.0~01

Something divided by as many times as it is existing should equal the likeness of 0 should it not?

[Anonymous No.5694796]

I'm not sure what you mean.

[Anonymous No.5694799]

I don't understand but I suspect this has something to do with the whole 1 = 0.99999. bullshit

[Anonymous No.5694801]

>>5694799

It's not bullshit, it's the sad truth.

[Anonymous No.5694807]

>>5694801
It is bullshit when /sci/ waste their time arguing over it.

[Anonymous No.5694819]

>>5694807
>mfw you're on the internet worrying about wasting time

Srsly though do you know how bad TV/Comp light is for studying?

[Anonymous No.5694965]

>divided by as many times as it is existing
Meaningless.

>the likeness of 0
Meaningless.

>0.0~01
Invalid notation for a non-real number.

[Anonymous No.5695062]

>>5694965
>Meaningless
Because in truth numbers are really composed of absolutely zip and we lovingly treat them as such, ignorantly at that.

>Meaningless
0.0~01, 1-1, 0.99..-0.99.. , what the hell does that equal anyway, any number in general, entirety when fully non-relative, anything we don't value, the list goes on in the subcategories and extensions

>Invalid notation
There isnt even a fucking notation for it, we use fucking etc, is this math or linguistics- we're dealing with a closed system of operationals determining infinite sets and you think we're anywhere near competant in our notation? NOT EVEN CLOSE

9478213435

Which one of those symbols is the operational?

Check.... Mate.

[Anonymous No.5695201]

I think the conjecture is still unsolved.

[Anonymous No.5695437]

>>5694781
our

[Anonymous No.5695735]

>>5695062
wut? are you trolling or are you actually trying to make a point? because if so, i didn' get a word beginning from the second >Meaningless.

>>5694781
>1/1 = 0.99.. or 0.0~01
i'm sorry, what's that supposed to mean? i fear i don' get the question. 1=0.99... is a true statement, 0.0~01 i have no idea what that is.

[Anonymous No.5695775]

0.9(9) -> 1
0.9(9) =/= 1
What's not to understand? And don't even start with this whole 1/3 thing.

[Anonymous No.5695780]

I'm assuming OP is saying something like this.

1/1 = 0.99...
0.99.../1 = 0.998...
0.998/1 = 0.997...

etc

[Anonymous No.5695786]

>>5695780
probably, but OP is retarded.

[Anonymous No.5695797]

[Anonymous No.5695831]

>>5695775
0.999...=1 fagget
x=0.999...
10x+9.999....
10x-x=9x=9
x=1

[Anonymous No.5695844]

1/3=0.3333..
2/3=0.6666..
3/3=0.9999..=1
Not, strictly speaking, a proof, but it appeals to intuition much better than the algebraic proofs that you can find in abundance on the internet.

[Anonymous No.5695851]

>>5695831
walks in a circle and calls it travel

[Anonymous No.5695856]

>>5695851
Still proved that shit bitch

[Anonymous No.5695861]

>>5695775
>0.9(9) -> 1

So you're saying <span class="math">\sum _{j=1}^{n}\left( \left( 0.1\right) ^{j}9\right)[/spoiler] tends to 1 as n tends to infinity right? Then as we're talking about when n = infinity then it fucking equals 1 because that's the definition of the limits of series you fucking dingus

[Anonymous No.5695869]

>>5695856
true... should organize your work better next time though

[Anonymous No.5695878]

>>5695869
My work is normally very organised, I'm just not used to doing proofs on an imageboard

[Anonymous No.5695899]

>>5695861
> when n=infinty

[Anonymous No.5695909]

>>5695831
Except 10=9.99..90
9=8.999.8

[Anonymous No.5695925]

>>5695909
Are you retarded?

[Anonymous No.5695947]

>>5695899
>he's never seen an infinity sign at the top of a sum
<span class="math">\sum _{i=0}^{\infty }a_{i}[/spoiler] is _defined_ as <span class="math">\lim _{n\rightarrow \infty }\sum _{i=0}^{n}a_{i}[/spoiler], which was exactly my point you cunt brush

[Anonymous No.5696216]

>>5695925
8.99..991 sry

Also, >>5695062
>0.99..-0.999.., wouldnt that equal -0.00..02?

[Anonymous No.5696229]

>>5695947
so when does n=infinity

[Anonymous No.5696271]

>>5696229
When you set it to be. Are you confused by the concept of variables?

[Anonymous No.5696300]

>>5696271
Hey, because translations comparisons are always the best way to learn, could you say that equation as a paragraph?

[Anonymous No.5696311]

>>5695947
>cunt brush

Wow, I have to be sure to use that one day.

[Anonymous No.5696317]

>>5696271
But infinity isn't a number.

[Anonymous No.5696363]

>>5696317
that's why we have limits, dumbass

[Anonymous No.5696366]

>>5696363
> setting a variable to infinity
> calls others dumbass

[Anonymous No.5696368]

>>5696300
A series is when you add up a sequence. Our sequence is 0.9, 0.09, 0.009 etc, or in other words <span class="math">\left( 0\cdot 1\right) ^{j}\times 9[/spoiler] for intergers j. We want to add up every single member of this sequence even though there are infinity of them, so this is going to get tricky. (I'm going to assume you know the sigma notation for sums here). We can work out <span class="math">\sum _{i=1}^{n}\left( \left( 0.1\right) ^{j}\times 9\right)[/spoiler] for any natural number n we want, (for example n = 3 gives us 0.9 + 0.09 + 0.009 = 0.999) but picking n = infinity is tricky because as this asshole has pointed out over and over >>5696317 infinity isn't strictly a number.

But! We can still do this as our sequence converges to zero (in a special way that I'm not going to go into), which means that when you add it up it's still bounded, even though we're adding an infinite number of numbers together. We still need to define our sigma notation a little more by borrowing from limits, specifically limits to infinity, which is when you inspect numbers when they get very big (for example, (x+1)/x will always be bigger than 1 because x+1 > x, but when you take the limit as x tends to infinity, <span class="math">\lim _{x\rightarrow \infty }\dfrac {x+1} {x}[/spoiler] = 1, which makes sense intuitively but I'm not going to go off course to prove it. Look up limits). Basically you evaluate the stuff on the right of the limit when the variable underneath gets as close as possible to the thing it's pointing at.

With sums and limits, it's defined (and makes complete sense) to define <span class="math">\sum _{i=0}^{\infty }a_{i}[/spoiler] as <span class="math">\lim _{n\rightarrow \infty }\sum _{i=0}^{n}a_{i}[/spoiler]. So we take the infinite sum to mean the limit of the bounded by n sum as n goes to infinity.

The argument started that because someone said 0.999... tended to 1 but wasn't equal to it, I was just saying that those two things were the same

>>5696317
Yes, correct. What's the problem here?

[Anonymous No.5696372]

>>5696366
see
>>5695947
also, take high school precal again

[Anonymous No.5696381]

>>5696372
it's ok if you fail but try failing upwards in the future

[Anonymous No.5696403]

>>5696381
If you're feeling angry about other people doing math on the internet I'm sure your school counselor has some free time to help you out

[Anonymous No.5696472]

>>5696368
> >>5695861
But it's still missing definition, it why are you reducing the infinitive definition to n when n itself has (n{x}) within it, lim is not accounting for the actual presence of the reduction and by extension saying 1=[{x}], is that intended?!

>pic related, 1 in limits definition

[Anonymous No.5696654]

bump