Dividing by zero, the truth (this is long!)

[Matt Simon]

Lolz mate, you are funny! Holes everywhere, but for starters:

- Summation is an binary operator, sure, by induction you can extend it to any natural number of summands, but then you go and "sum from 0 to infinity" OMG!!! Both your calculus and your algebra teacher should be ahsamed! That is a series, and you are not using the sum, but finding a limit.

- OMFG mate, Sigma (n^2) with n goig from 1 to infinity is a non convergent series! Thus you can't do E(n^2)*2 - E(n^2)*1!!!

I can tell you like this stuff, and you might be good at it if you try! But stop doing make belive and actually study math.

Edit: About the other stuff. It does sound like we are using "language", but actually function, well-defined, real number, divisor, field, ring, and all that crap are math concepts defined with logic rigor; we could translate that to simbolic logic and use only those signs, and by we i don't meant me, because i never took a simbolic logic class, but a dude that has could

actually my calculus teacher would have ignored it, but my differential equations teacher would have said i showed you that one, good job remembering the subject of chapter 3.
as for calculus, i have taken up through calc 3, which i finished with a 79% after spending 72 hours to finish my entire online course.
i don't just know how to talk about it, i can speak it. just have some difficulty typing it.
and yes accidentally mixed how i wrote it. the series should be
E(2^n)
so
E(2^n) = (1 + 2 + 4 + 8 + ...)= infinity
x*1= x
2-1=1
x*(2-1)=x
x*2 - x*1=x
E(2^n)*2 - E(2^n)*1= infinity
E(2^n)*2 - E(2^n)*1= (2 + 4 + 8 +...) - (1 + 2 + 4 + 8 + ...)
E(2^n)*2 - E(2^n)*1= -1 + ( 2 -2 + 4 - 4 + 8 - 8 + ...)
E(2^n)*2 - E(2^n)*1= -1 + ( 0 )
E(2^n)= -1
infinity = -1
one of those mistakes very easy to notice when writing by hand because the power should be the small one to the upper right of the base.
for more information refer to
http://en.wikipedia.org/wiki/Evaluating_sums
and http://en.wikipedia.org/wiki/Taylor_series

also the language thing was a reference to Terry Pratchett character arch-wizard Truman.

 

[Tanakh]

x*2 - x*1=x
E(2^n)*2 - E(2^n)*1= infinity

also the language thing was a reference to Terry Pratchett character arch-wizard Truman.

Ahh, Pratchett, one of the few, very few, fantasy writers that I regret not having read. Lend me some books!!!1

Also, the problem with the proof is that you take a valid statement from x in R, and then you use it for a series that doesn't converge to R; that's why you end up with nonsense, you can't pass from the first line I quoted to the second.

Also ODE!! How i loathed to teach that subject! Why did i never got lineal algebra or topology! Sad panda.

 

[Sprinal]

As I am starting UNI this month... I feel like its going to be hard.....

Okay I did well at maths in High School (was the only one to actualy understand the Binomial theorem). Yet this....

I'm not even going to bother until 2nd year at least.

 

[Matt Simon]

x*2 - x*1=x
E(2^n)*2 - E(2^n)*1= infinity

also the language thing was a reference to Terry Pratchett character arch-wizard Truman.

Ahh, Pratchett, one of the few, very few, fantasy writers that I regret not having read. Lend me some books!!!1

Also, the problem with the proof is that you take a valid statement from x in R, and then you use it for a series that doesn't converge to R; that's why you end up with nonsense, you can't pass from the first line I quoted to the second.

Also ODE!! How i loathed to teach that subject! Why did i never got lineal algebra or topology! Sad panda.

What!! how can you not like DivEq. i mean all through the calculus's they have you using round about methods to problems that when you learn them in physics or engineering they are actually quite simple and easy to solve. and then finally you get to the year where your taking DivEq and intro to electrical engineering and it switches, you find yourself complaining to your engineering professor that half the time instead of going through all these intermediary equations to find everything about this circuit, we could just sum it up into a rather simple differential equation.
then again every class period was 3 hours that would be spent writing 20 pages of notes.
that would suck to teach, you get carpel tunnel a lot.

although i am a little confused, the taylor series E(2^n) would basically become 1+2+4+8+16+32+64+128+246...
so since in its first couple test conditions it keeps increasing then if you continued to add successive conditions where the value used for n is incremented to infinity, the resulting sum would be infinity right.
the argument is basically since all your technically doing to the equation is multiplying it by 1 then you haven't actually changed the equation, except that if you were to write it out it quickly becomes apparent that since every element in the series multiplied by two will be matched by a negitive element in the other series the only remaining value becomes the negitive 1
2-1=1
E(2^n)=E(2^n)*1=E(2^n)*(2-1)=E(2^n)*2-E(2^n)=infinity
its just something my diveq teacher showed us after she kept pointing out the order of operation violations in attempts to disprove mathematics students brought her.

 

[Tanakh]

What!! how can you not like DivEq.

although i am a little confused
2-1=1
E(2^n)=E(2^n)*1=E(2^n)*(2-1)=E(2^n)*2-E(2^n)=infinity
its just something my diveq teacher showed us after she kept pointing out the order of operation violations in attempts to disprove mathematics students brought her.

Differential Equations? I was a little lazier back then and hated to do all the calculus work that was involved in order to prove the framework needed to work. Once that was done, the examples were indeed fun and beautiful. Though honestly i always did more biological, financial and kinetic examples over the electromagnetic ones.

As for the confused part, you have proven that Sigma (2^n) n from 0 to infinity = infinity. So when you are writing E(2^n)*2 - E(2^n) what you have written is infinity - infinity; in ODE, Calculus and so forth every time we end up with a division or rest of infinity figures we just stop that route and look for another one, because that is undetermined. To sum up you know infinity = E(2^n) = E(2^n)*1 = E(2^n)*(2-1) BUT, you dont know E(2^n)*(2-1) = E(2^n)*2 - E(2^n) because infinity = E(2^n) and infinity * (2-1) doesn't behave like a real number, IE, you can't distribute the multiplication.

 

[Helmholtz Watson]

After reading the title, I am reminded of something I saw on TV Tropes....

If x = 1 and y = 1
Then 2(x2 - y2) = 0
And 5(x ? y) = 0
Which is to say, 2(x2 - y2) = 5(x ? y)
Now divide each side of this equation by (x-y): [2(x2 - y2) = 5(x ? y)] / (x ? y)
Which comes to 2(x + y) = 5
But (x + y) = (1 + 1)
Which means that 2*2 = 5.

 

[CrystalShadow]

But then you really end up going into the definitions of what actually constitutes proof.

Proof: The sublte art of talking your teachers or peers into accepting that the stuff you say happens indeed happens! Mora akin to talking that gal you like into a drink with you than to discovering the "UNIVERSAL TRUTH".

Ur turn.

Proof: What we use to convince ourselves something makes sense, when we don't actually have a clue what's going on.

 

[Tanakh]

Proof: What we use to convince ourselves something makes sense, when we don't actually have a clue what's going on.

And that has annoyed people how? I mean... i dunno, maybe some super sensitive teens or students of logic 101... but damn, having a hard time seeing it.

Though TBH i think we need to have SOME clue of what's going on to give a proof. It's like doing a swindle selling sugar as vitamin supplements, sure you don't have to even know what's a vitamin, but the more you do know the better chances to pull it off

Then there are the constructive proofs, those are my favourite ones

 

[CrystalShadow]

Proof: What we use to convince ourselves something makes sense, when we don't actually have a clue what's going on.

And that has annoyed people how? I mean... i dunno, maybe some super sensitive teens or students of logic 101... but damn, having a hard time seeing it.

Though TBH i think we need to have SOME clue of what's going on to give a proof. It's like doing a swindle selling sugar as vitamin supplements, sure you don't have to even know what's a vitamin, but the more you do know the better chances to pull it off

Then there are the constructive proofs, those are my favourite ones

Wait, did I imply anything about annoying people? (looks back at own post). Oh right. I see now.

No, what I just said is merely a joke.

If you mean, what annoys people? The worldview that derives as a natural consequence of requiring a very thorough definition of what can be considered proof.

This is basically the weakest form of solipsism. -> The only thing you can prove to actually exist is your own personal experiences. Anything else is speculative.

(The strong form of solipsism then goes on to assert that therefore this is all that actually exists. But that's a bit silly.)

That particular notion rather annoyed a few people I was talking to.
Particularly someone who claimed to be an atheist on the grounds that he only believed in things which had evidence for their existence...
(or something to that extent. I couldn't quite get him to explain his position in a way that entirely made sense to me.)

Of course, I then proceeded to state that what he considered 'proof', I considered uncertain...

Which is where the annoyance started to become evident.
(I guess someone doesn't want to spend any time actually giving any consideration to the nature of truth itself? Eh. Whatever. XD)

 

[Tanakh]

Particularly someone who claimed to be an atheist on the grounds that he only believed in things which had evidence for their existence...
(or something to that extent. I couldn't quite get him to explain his position in a way that entirely made sense to me.)

Of course, I then proceeded to state that what he considered 'proof', I considered uncertain...

Which is where the annoyance started to become evident.
(I guess someone doesn't want to spend any time actually giving any consideration to the nature of truth itself? Eh. Whatever. XD)

Those damn regular flavour atheist! More strict in the dogma of their bleifs than the common religion follower

I like the smart atheism thoug.
- Does God exsist?
- No!
- How do you know?
- Humm, don't tell the police, but I killed a while ago with this german with a crazy mustache.

 

[Matt Simon]

What!! how can you not like DivEq.

although i am a little confused
2-1=1
E(2^n)=E(2^n)*1=E(2^n)*(2-1)=E(2^n)*2-E(2^n)=infinity
its just something my diveq teacher showed us after she kept pointing out the order of operation violations in attempts to disprove mathematics students brought her.

Differential Equations? I was a little lazier back then and hated to do all the calculus work that was involved in order to prove the framework needed to work. Once that was done, the examples were indeed fun and beautiful. Though honestly i always did more biological, financial and kinetic examples over the electromagnetic ones.

As for the confused part, you have proven that Sigma (2^n) n from 0 to infinity = infinity. So when you are writing E(2^n)*2 - E(2^n) what you have written is infinity - infinity; in ODE, Calculus and so forth every time we end up with a division or rest of infinity figures we just stop that route and look for another one, because that is undetermined. To sum up you know infinity = E(2^n) = E(2^n)*1 = E(2^n)*(2-1) BUT, you dont know E(2^n)*(2-1) = E(2^n)*2 - E(2^n) because infinity = E(2^n) and infinity * (2-1) doesn't behave like a real number, IE, you can't distribute the multiplication.

true, technically its infinity-infinty but all this algerbra stuff is really based of ignoring the potential value of something and moving around until you get it to a spot you like it and then declare it to take its real value so basically think of
E(2^n)*2-E(2^n)
as
2x-x
and just for fun treat x like a function call in a program so instead of returning this equation that definitely equals infinity we get this theoretical infinite array of data
so as i would write it in a program
inf_int sum=x(2)+x(-1);
so each element of this array[infinity] is filled with a solution for E(2^n) making two sets of data which are
array1(2,4,8,16,...)
and
array2(-1,-2,-4,-8,-16,...)
then we preform the addition of these two sets of data
(-1+2-2+4-4+8-8+16-16+...)
which it would conclude as
(-1)
of course at this point we could point out that technically array2 has one more element than array 1 buts its hard to say if that means their is an extra value of E(2^(infinity+1)) left over along with the -1 because conceptually infinity should be the exact same distance from every number meaning that no matter what data point you start at their is still only an infinite number of other numbers left.
but the primary point remains that it really doesn't matter what the acuatual value is, if you want to treat 3+5 different than its immediate value of eight you can and most algebra manipulation is kind of based on the assumption that we like to do that.

 

[Matt Simon]

Particularly someone who claimed to be an atheist on the grounds that he only believed in things which had evidence for their existence...
(or something to that extent. I couldn't quite get him to explain his position in a way that entirely made sense to me.)

Of course, I then proceeded to state that what he considered 'proof', I considered uncertain...

Which is where the annoyance started to become evident.
(I guess someone doesn't want to spend any time actually giving any consideration to the nature of truth itself? Eh. Whatever. XD)

Those damn regular flavour atheist! More strict in the dogma of their bleifs than the common religion follower

I like the smart atheism thoug.
- Does God exsist?
- No!
- How do you know?
- Humm, don't tell the police, but I killed a while ago with this german with a crazy mustache.

all this time i had assumed neiztche was saying "you christian have killed him" refering to a member of the religion but he meant it as a proper noun.
damn German and their grammatical rule that all nouns are capitalized. if he had been an English writer he would have deffinately written "and you Christian have killed him" and we would know immediately he meant someone he knew named Christian.
Your quite the sneaky bastard Tanakh, or should i say... Christian.

 

[CrystalShadow]

Particularly someone who claimed to be an atheist on the grounds that he only believed in things which had evidence for their existence...
(or something to that extent. I couldn't quite get him to explain his position in a way that entirely made sense to me.)

Of course, I then proceeded to state that what he considered 'proof', I considered uncertain...

Which is where the annoyance started to become evident.
(I guess someone doesn't want to spend any time actually giving any consideration to the nature of truth itself? Eh. Whatever. XD)

Those damn regular flavour atheist! More strict in the dogma of their bleifs than the common religion follower

I like the smart atheism thoug.
- Does God exsist?
- No!
- How do you know?
- Humm, don't tell the police, but I killed a while ago with this german with a crazy mustache.

Oh, that wasn't even the worst example.

I got into an argument about the certainty of scientific theories, and, implying they contained a certain amount of uncertainty...

Got as a response that I should 'prove' the theory of gravity by jumping off a tall building...

Ah, some people. Why bother to consider what someone is actually saying to you when you can just tell them to kill themselves? XD