/sci/ - Science & Math

*-1/12

what are u talking about it's 14

>>10294026
You should stop taking the bait. Adding up positive numbers will never get you a negative result, the method to get that number is not the definition of summation.

Stop watching Numberphile videos and read an actual calculus book.

This may help
https://plus.maths.org/content/infinity-or-just-112

An infinite series is a function of the infinite list of terms, i.e. sequence, that you want to add up. This summation function has some nice properties. Linearity is one property, and it means that the sum of two infinite series is the infinite series of the term-by-term sums. There's also a property that you can pull a finite number of terms out of the infinite sum as a finite sum, which is just arithmetic. This summation function is not defined for all sequences, obviously.

But then we can ask: what other functions can we define on sequences that share the same properties as infinite series? That leads to generalized summation methods. If you change the definition of what you mean by "infinite series", you can get finite values for divergent series without screwing up convergent series.

>>10294059
stop reading a baby calculus book and read an actual complex analysis book

>>10294051
>Adding up positive numbers will never get you a negative result
you have no basis to say that
adding up infintely many rationals can get you an irrational

>>10294026
>Ok, so I just do not understand why the heck is 1+2+3+4+5... = 1/12
because the "equals" sign in that does not mean what you think it means. it's not the notation you're assuming it is

>>10294094
>you have no basis to say that
>adding up infintely many rationals can get you an irrational
People say this a lot, but there's a big difference. Rationals are not closed. But rationals and reals are both ordered fields, and addition respects ordering while generalized summation doesn't.

>>10294103
Rationals are not complete*, I'm a brainlet.

>>10294103
>and addition respects ordering
is that binary addition youre speaking of?

>>10294026
>>10294084
>https://plus.maths.org/content/infinity-or-just-112
Woow so seriosly a rtard said that in jewtube? I think the WORST of that faggots are the one with quentum mechanics. You can see all they say is false using basic logic. They prob dont even know what center of mass is.

>>10294109
Convergent series also respect ordering.

This is why math is fucking useless. Bunch of bullshit that nobody cares about + doesn't help people such as why does infinitely adding positive number give you -1/12. Sorry fags, anything past diffy q doesn't even matter and thats being generous.

>>10294100

>because the "equals" sign in that does not mean what you think it means. it's not the notation you're assuming it is

Ahh...so...the "equals" sign can sometimes have a different meaning? Gosh, and there I was thinking it could only mean "equal"...

Shut the fuck up, you immensely ignorant pig fuck of a retard.

>>10294127
seething

>>10294103
Adding the part I didn't state explicitly: limits respect non-strict ordering.

>>10294158
it's not literally saying if you add every integer you end up with a negative number, it's saying that if you apply some math tricks you can associate the value of -1/12 with that particular infinite divergent series. it's the answer you get if you analytically extend the riemann zeta function so you can apply it to -1

>>10294158
He's right though.

>>10294026
>>10285455

>>10294187
>>10294206
>analytic continuations defining property is that its equal to the original
>"no! its totally not the same thing!"

>>10294100
>equals sign does not mean equals

>>10294103
>Rationals are not closed...
Under what? Finite or infinite summation?
>addition respects ordering
Not under infinite summation, brainlet.
https://en.wikipedia.org/wiki/Riemann_series_theorem

>>10294119
Only absolutely convergent series respect ordering.

>>10294187
>it's saying that if you apply some math tricks
Same as any other infinite series retard

>>10294051
>the method to get that number is not the definition of summation
There's no one "the" definition of summation

>>10294220
>>10294225
"Ordering" as in ordering of real numbers. Seriously, how about you look at the context of ordered fields I was talking about.

>>10294243
What does that have to do with any of this?

>>10294247
It should be obvious that it has to do with "adding positive numbers" to get a negative number that was mentioned earlier in the thread, and how generalized summation methods abandon ordering that the partial sums definition preserves.

>>10294026

>1+2+3+4+5... = 1/12.
lol lol lol

>but imaginary numbers are sooo useful!
lol lol lol

>0/0 is undefined, except when we dont want it to be!
lol lol lol

>√2
lol lol lol


Jesus Fucking Christ. I have had enough of this bullshit. Math is just a seriously fucked up mess. Why people tolerate this utter illogical bullshit is incomprehensible.

Its should have been totally obvious, for the past 2000 FUCKING YEARS, that the most basic concepts, the most fundamental axioms are VERY FUCKING WRONG and result in these intellectual obscenities we witness today.

>b...but Anon, that is just the way it is! It works! It gets us to the moon and back!

The fact that so many of you pansies defend this nonsense just shows that much of humanity lacks the creative thought required to engender a revolutionary new conceptual approach to math.

FUCK NUMBERS! YES FUCK THEM! Every since mankind started touching of his fingers and toes we have been on the wrong track! ITS A DEAD END! It results in the bullshit we see here.

Its time to start anew. With a clean slate. To throw away all these Neanderthalic superstitions we call "math" and actually formulate an entirely new system of logical evaluation of existence.

Viva la revolution!

DEATH TO THE NUMBERS!

>>10294094
>adding up infintely many rationals can get you an irrational

>>10294103
>>10294252
Limit-of-partial-sums summation may respect ordering but it doesn't respect commutativity which is an even more fundamental property of a field. So your point is stupid.

>>10294267
It respects any finite number of commutations.

>>10294270
lmao

>>10294265
>

>>10294274
It's fine if you don't care, but it's true.

>>10294103
Cesaro summation respects ordering.

>>10294308
That's true, I was being careless. My mulligan statement would be: any method that sums the series in the OP doesn't respect ordering.

>>10294284
every sum respects a finite number of commutations

>>10294343
Which is why I wasn't the one to bring up commutation, because my point was about ordering.

>>10294349
you were the one who brought up finite commutation
ordering is still unrelated to this

>>10294355
Finite commutation was a response to "who cares about ordered fields because commutation doesn't hold". In fact, I could just as well have said that the sum of two converging infinite series is commutative even though terms within a single series aren't. Either way, commutativity wasn't my point, ordering was. And summing the series in the OP requires losing ordering.

>>10294364
i still fail to see why i should worry about losing ordering
you dont determine divergent series based on their upper bounds or anything

>>10294387
The property is there whether you care or not.

>>10294398
so you have no complaint except liking ordering
just say that from the beginning

>>10294405
See:
>>10294284

>>10294407
0 loses the property of having a multiplicative inverse
guess we better abandon it
real shame, its done us well

>>10294408
Indeed, you have to make a choice to either abandon zero or abandon everything having a multiplicative inverse.

>>10294412
exactly
and youre trying to make the point of having ordering at the expense of all else
you like ordering
again, just say that from the beginning

>>10294266
Interesting, but how do you propose we start from scratch in building a new fundamental idea of mathematics? What are the real axiomatic concepts that we should focus on instead of axioms that involve the concept of numbers?

>>10294421
>and youre trying to make the point of having ordering at the expense of all else
I never said generalized summation was bad because it loses ordering. I said normal summation preserves ordering and the sum in the OP doesn't.

>>10294429

Well yes, I admit that's the tricky part. Ive though a great deal about this over the past ten years, and every time I find my thinking screwed up by my acquired preconceptions, what I've been exposed to, what I have been taught. Basically I need a mind wipe.

One thing we could do is have a bunch of bright people all isolated on some island, with their memories of anything about math completely stripped bare. Even anything to do with math in linguistics also removed. They are unable to express anything in terms of present maths. They want a banana, some bananas, lots of bananas, a transfer of bananas from one person to another. A set of bananas put aside for a rainy day? No. They dont even have concepts such as these in their heads.

They must start from scratch, in complete isolation for the rest of humanity, to develop a new language to describe and manipulate the world around them.

Perhaps they would end up just replicating what we already have, perhaps just doing that would take countless generations, in which case its all a failure.

In any case such a scenario is impossible to enact even if you could find the volunteers willing. So we are stuck with what we have got, which makes the task that so much more difficult.

>>What are the real axiomatic concepts that we should focus on instead of axioms that involve the concept of numbers?

Another possible option is pure geometry without measurement. Patterns expressed in terms of relationships instead of numbers.

Listen, I admit I'm not that smart, but I know a train wreck when I see one. Math is a train wreck and I hope some day some incredibly clever people will see it as such but also develop the conceptual breakthroughs we need to move past this mess.

Supposedly infinite series often only have as little as five elements and some dots.

>>10294477
Why do you say math is a "train wreck" considering it's wildly successful?

>>10294477
>Patterns expressed in terms of relationships instead of numbers.
So set theory.

>>10294754
he could also mean group theory

>>10294026
https://youtu.be/sD0NjbwqlYw?t=10m