/sci/ - Science & Math

>>14827235
>Is
>2 + 4 + 8 + 16 + 32 + ... =
>Bigger than
>1 + 2 + 3 + 4 + 5 + ... =
>?
Well....
32 is bigger than 5 so im gonna go ahead and say yeah

These are some very interesting questions you've posted. Types of questions sometimes people even in 2nd year university mathematics still don't get a clear answer for.

From my understanding, they are both infinity, though infinity, is not technically a normal "number."

In mathematics you might have some sort of equation y = 2x, it's not seen as standard to just plug in a value of x = [math] \infty [/math], as it's not really considered a normal number. Though if you were to plug in x = [math] \infty [/math], me and you would both easily know the answer is y = [math] \infty [/math]. In my mathematics class, I wouldn't be marked down for writing this, as me and the lecturer would both know what I meant.

So this is where it gets a bit odd, because sometimes, you can sort of treat it like a number, but sometimes you can't.

So with that being said, you can imagine that it's just a type of special number, with the basic definition just being that, infinity is something which is bigger than any other number you could pick.

It has a limitless value, and there is nothing bigger than it. With that being said, both of those equations you picked are infinity. Infinity cannot be reached, (If you ever reach a destination there is an end, but infinity is limitless, meaning it has no end).

If you take a partial sum, and you stop once you've reached the 100th consecutive number, for example, in the sum 1 + 2 + 3 + 4 + 5 + 6 + ... + 100, then yes you will have a determinable sum, but this is not infinity, and this applies for all sum equations you can think of.

For the last equation you posted, the overall equation doesn't necessarily "equal 1," as we've said, "infinity," can never be reached. But for this infinitely long sum, it "pretty much" does just equal 1. Or at least, it infinitely gets closer and closer to 1. (which is where limits for math comes in)

0.99999999999... with an infinite amount of 9s after the full stop, does basically equal 1 right? Probably.

>>14827235
>Is
>2 + 4 + 8 + 16 + 32 + ... =
>Bigger than
>1 + 2 + 3 + 4 + 5 + ... =
>?
Neither of those converge to a value, so your question is meaningless.

>Are they both infinity?
No.

>surely this sum never reaches 1
It converges to 1 and is 1. "Reaches" has no meaning in this context.

Another interesting question to note is that [math] (1/3)\cdot3 = (3/3) = (0.33333...)\cdot3 = 0.9999999... [/math]

But, [math] (3/3) = 1 [/math] right? So sometimes it's best just not to overthink it, because infinity is a useful concept, that just sort of works. And believe me when I say that it's been explored to it's full potential already.

>>14827292
imo it's not a meaningless question, as these are similar concepts that get explored sometimes like the concept of "Countably infinite," and "Uncountably infinite."

But realistically, exploring it too much doesn't provide any helpful insights which will help solve some crazy equation.

1/inf=0

>>14827312
Maybe this just bullshit but anyway:
Let's say
[eqn]2+4+8+16+32+... = S_1[/eqn]
and
[eqn]1+2+3+4+5+...=S_2[/eqn]
If we subtract [math]S_2[/math] of [math]S_1[/math] term by term (because why not) we get
[eqn]S_1 - S_2 = (2-1) + (4-2) + (8-3) + (16-4) + (32-5)+...=D[/eqn]
given that each term of the sequence is positive then [math]D>0[/math] and we can say [math]S_1>S_2[/math]
on the other hand
[eqn]S_2 - S_1=(1-2) + (2-4) + (3-8) + (4-16) + (5-32)+...=E[/eqn]
each term is negative, then [math]E<0[/math] and [math]S_2<S_1[/math]
But I guess this can change if changing the way you substract one sequence from the other, like playing with conditionaly convergent series, you can come up with almost any result you want, like the [math]\frac{-1}{12}[/math] meme.

>>14827292
Do you know the grammatical usage of the english word "converge" or do you just believe it's a maths concept with your own headcanon definition?
Infinite sums do not converge in present or past tense. They are converging. As in, converging towards something. Or they are diverging. It should be well reasonable to you that neither "converging" or "diverging" are the fucking word "equals" too, so you should understand that different words mean different things and maybe practice learning more of your own language rather than continuing to fuck up conversation in the English language.

>>14827303
1/3 isn't equal to 0.333..
1/3 is greater than 0.333...

>>14827235
infinity isn't real

>>14827235
If you take first step, it is bigger
If you take infinite steps, it's infinite steps

>>14827342
>because why not
subtraction is a sure way to get things wrong
https://www.youtube.com/watch?v=U0w0f0PDdPA

>>14827353
well duh, that's in the definition

>>14827346
1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

>>14827720
0.333... is an artifact of being unable to fully solve the input form 1/3.

1/3 [ = ]
0.3 (is this correct? no. continue)
0.33 (is this correct? no. continue)
0.333 (is this correct? no. continue)
0.3333 (is this correct? no. continue)
0.33333 (is this correct? no. continue)
0.333333 (is this correct? no. continue)
0.3333333 (is this correct? no. continue)
0.33333333 (is this correct? no. continue)
...
0.333... (is this correct? no. continue)

the degree of incorrectness in the attempt to solve is that the result is always less than the target desired end result, aka it's less than equal.

0.333... < 1/3
3(0.333...) < 3(1/3)
0.999... < 3/3

it's intuitive when understanding no true infinite of numbers, as there will be real world cutoff points of finite determinable necessity.
if the units here were meters from the point of view of a discerning human eye, even nanometers might be too much, but could suffice
0 meters +
0.3 meters (30 centimeters) +
0.03 (3 centimeters) +
0.003 (300 millimeters) +
0.0003 (30 millimeters) +
0.00003 (3 millimeters) +
0.000003 (300 micrometers) +
0.0000003 (30 micrometers) +
0.00000003 (3 micrometers) +
0.000000003 (300 nanometers) +
0.0000000003 (30 nanometers) +
0.00000000003 (3 nanometers) =
0.33333333333

>>14827751
>an artifact
nah it's the solution
grow up

>>14827751
>0.3 (is this correct? no. continue)
>0.33 (is this correct? no. continue)
>>0.333 (is this correct? no. continue)
>>0.3333 (is this correct? no. continue)
>let's pretend finite is infinite

>>14827803
>>14827799

the infinity you believe exists is an artifact of your stupidity and lazy inability to continue counting, substituting true knowable accuracy with false unprovable guesses.

>>14827837
>unprovable
it's an axiom, retard.
and it just werks

>>14827345
>They are converging. As in, converging towards something.
Take your meds, time has absolutely no place in mathematics

>>14828165
lol, idiot
learn2read

>>14828172
Learn some basic logic first

>>14827751
0.333... exists because you are operating in base 10, your post is pseud beyond belief

>>14828174
"Infinite sums do not converge in present or past tense."
You're an illiterate idiot.

>>14828212
Cope, go back to calc 1 brainlet

>>14828215
>i have no argument

>>14827345
>Do you know the grammatical usage of the english word "converge" or do you just believe it's a maths concept with your own headcanon definition?
It's a well defined mathematical concept, which also conforms to the casual definition. Why are you getting worked up about mathematical definitions in a math thread?

>Infinite sums do not converge in present or past tense.
Convergence just means that the limit of its partial sums exist. Where do you see time in that definition? Either a series is convergent or it isn't.

>It should be well reasonable to you that neither "converging" or "diverging" are the fucking word "equals" too
Right, because there are different contexts for convergence in math. Only in the context of series does convergence to a limit imply equality to that limit.

>>14827751
>0.333... (is this correct?
Yes.

>>14828178
expansion numbers are not real numbers. if the numbers continue without an end after the decimal point, it's a fucking dumb nigger number and essentially
"actually imaginary". retarded rules of assumption (like rounding) need to be made to make up for the faggot inaccuracy, sullying the distinct assumption of the perfection of math or math as a universal language.

>>14828229
>>14828212
>"tImE dOeS nOt ExIsT"
take your meds

>>14828285
>hand waving intensifies
lol

>>14828285
>>"tImE dOeS nOt ExIsT
Who are you quoting?

>>14828285
>a quirk of the chosen basis means the number doesn't exist
meds, now

>>14827714
>subtraction is a sure way to get things wrong
yup, I'm aware of that. that's why I mentioned the conditional convergent stuff. I'll check that video too anon.

>>14827235
compare the growth rates of the two sums
partial sums of the second are o(partial sums of the first)

>>14827291
>Types of questions sometimes people even in 2nd year university mathematics still don't get a clear answer for.
This is a first year math problem in the US. You would find both series, then determine if one is bounded by the other, or a known series. Yes there are different values of infinity/divergence.

t. Its my first semester at a US public school.

>>14828900
there are not different values of infinity.

>>14830348
there are an infinite amount of infinities
https://www.youtube.com/watch?v=BBp0bEczCNg
https://www.youtube.com/watch?v=FVZqPaH94qU

>>14827235
Infinity is just a placeholder for "numbers that don't end", it's really not that complicated, why write out an infinite amount of numbers when you could just write one symbol and be done with it

>>14827235
q + q^2 + q^3 + .. = q/(1-q)
Plug in q=2 to get
2 + 4 + 8 + 16 + 32 + ... = -2
which is smaller than 1 + 2 + 3 + ... = -1/12

>>14830473
https://youtu.be/sZ2qulI6GEk?t=3m30s

>Does one sum reach infinity before the other sum?
It's a sum, not a function.
2 + 4 + 8 + 16 + 32 + ... = a
is 64 at [2, 32]
1 + 2 + 3 + 4 + 5 + ... = b
is 527 at [2, 32]
The ratio should stay the same everywhere, so b/a ≈ 8

>>14827235
nobody cares
also related to - what's that term, for the branch of math that says something about irrational numbers not fitting in the simulation (fag talk) but based on some ideas by someone else about rationalism or realism? i forget

>>14827303
> interesting
not interesting

>>14830368
there is 1 infinity and every real number is infinitely away from it, that all real numbers are equal to each other compared to infinity, that all real numbers are equal to 0 relative to infinity.
for numbers to have value, infinity can not be a number or a mathematical object with relation to numbers.

>>14827235
>Is
>2 + 4 + 8 + 16 + 32 + ... =
>Bigger than
>1 + 2 + 3 + 4 + 5 + ... =
>?
No. They're both infinity.

>>14831076
>mathematical object with relation to numbers.
it's bigger
duh

>>14828900
And with that, anon solves the continuum hypothesis.