God and Math

[HRE]

0 = 0 + 0 + 0 + 0 + 0 + 0 +...
= (1 - 1) + (1 - 1) + (1 - 1) +...
= 1 - 1 + 1 - 1 + 1 - 1 +...
= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +...
= 1 + 0 + 0 + 0 +... = 1

Thus, something may be created from nothing.

Thus, God does not need to exist.




Now Mods, hold on a minute, I beseech you. This should perhaps go in GA, but this is perhaps the most educated area of this website, and since this applies directly to upper level mathematics, I beg that it should stay here.

At least let it run for a 24 hours...and see where it goes.

Thank you.

 

[Ampoliros]

0 = 0 + 0 + 0 + 0 + 0 + 0 +...
= (1 - 1) + (1 - 1) + (1 - 1) +...
= 1 - 1 + 1 - 1 + 1 - 1 +...
= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +...
= 1 + 0 + 0 + 0 +... = 1

Bah, you're off by one ! *shakes fist at infinite series*

 

[Anjinsan]

In other news, Infinity divided by infinity = 12

 

[The Seeker]

0 = 0 + 0 + 0 + 0 + 0 + 0 +...
= (1 - 1) + (1 - 1) + (1 - 1) +...
= 1 - 1 + 1 - 1 + 1 - 1 +...
= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +...
= 1 + 0 + 0 + 0 +... = 1

My brain just crawled out of my ear in a desparate attempt to escape this very scary peice of maths, can somebody explain this for me?

Edit: Surely this is wrong:

1 - 1 + 1 - 1 + 1 - 1 +...=1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +...

Shouldn't it read:
1 - 1 + 1 - 1 + 1 - 1 +...=1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +...-1
Or have I missed the point altogether?

 

[DrunkenWrestler]

The last one says 0=1.

 

[Ampoliros]

My brain just crawled out of my ear in a desparate attempt to escape this very scary peice of maths, can somebody explain this for me?

Right-o!

0 = 0 + 0 + 0 + 0 + 0 + 0 +... (this makes sense; 0+0+0 plus however many zeros you like is still zero)
0 = (1 - 1) + (1 - 1) + (1 - 1) +... (he substitutes (1-1) in for zero, as they're equal)
0 = 1 - 1 + 1 - 1 + 1 - 1 +... (removing the parentheses)
0= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +... (recombining them into parens)
0 = 1 + 0 + 0 + 0 +... = 1 (result!)

It seems all handy and right, but it is off by one...to put it simply, you cant add the series I think because the index is off. You're combining the 'first' negative one with the 'second' positive one. Its easier to explain with sigmas, but the board doesnt really make putting in large greek letters easy.

 

[comana]

Ummm

Do we have a geek forum?

 

[The Seeker]

Right-o!

0 = 0 + 0 + 0 + 0 + 0 + 0 +... (this makes sense; 0+0+0 plus however many zeros you like is still zero)
0 = (1 - 1) + (1 - 1) + (1 - 1) +... (he substitutes (1-1) in for zero, as they're equal)
0 = 1 - 1 + 1 - 1 + 1 - 1 +... (removing the parentheses)
0= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +... (recombining them into parens)
0 = 1 + 0 + 0 + 0 +... = 1 (result!)

It seems all handy and right, but it is off by one...to put it simply, you cant add the series I think because the index is off. You're combining the 'first' negative one with the 'second' positive one. Its easier to explain with sigmas, but the board doesnt really make putting in large greek letters easy.

Thanks, I had a feeling that the maths were off here (see my edit)

 

[The Seeker]

This kind of reminds me of a slightly geeky puzzle I saw a while ago:
x = y
x^2 = xy
x^2 - 2xy = -xy
2(x^2) - 2xy = x^2 - xy
2(x^2 - xy) = x^2 - xy
2 = 1

 

[Battie]

*brain pops*

I'm sure we disproved that in Calculus... *digs through old book*

 

[Juvenal]

Right-o!

0 = 0 + 0 + 0 + 0 + 0 + 0 +... (this makes sense; 0+0+0 plus however many zeros you like is still zero)
0 = (1 - 1) + (1 - 1) + (1 - 1) +... (he substitutes (1-1) in for zero, as they're equal)
0 = 1 - 1 + 1 - 1 + 1 - 1 +... (removing the parentheses)
0= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +... (recombining them into parens)
0 = 1 + 0 + 0 + 0 +... = 1 (result!)

It seems all handy and right, but it is off by one...to put it simply, you cant add the series I think because the index is off. You're combining the 'first' negative one with the 'second' positive one. Its easier to explain with sigmas, but the board doesnt really make putting in large greek letters easy.

You can't add the series because it doesn't converge.

Okay, I can't resist, blame it on too many years teaching freshman calc ... all right, class, what is the first test for convergence of an infinite series?

 

[Juvenal]

This kind of reminds me of a slightly geeky puzzle I saw a while ago:
x = y
x^2 = xy
x^2 - 2xy = -xy
2(x^2) - 2xy = x^2 - xy
2(x^2 - xy) = x^2 - xy
2 = 1

... if and only if x squared - xy is not zero.


Now, find the error ...

Girls take up time and money and time is money so

girls = time * money
time = money
girls = money * money

But money is the root of all evil so

money = square root (evil)
evil = money * money

But then

Girls = evil




Now that can't be right, can it?

 

[Bargainfluger]

This kind of reminds me of a slightly geeky puzzle I saw a while ago:
x = y
x^2 = xy
x^2 - 2xy = -xy
2(x^2) - 2xy = x^2 - xy
2(x^2 - xy) = x^2 - xy
2 = 1

LET ME AT IT!

The flaw is in between steps #5 and 6.

2(x^2 - xy) = x^2 - xy

It actually becomes quite simple if you plug in numbers:
Let x=2 and y=2

2(2^2 - (2)(2)) = 2^2 - (2)(2)
=
2(4-4)=4-4
2(0)=0

To get from step 5 to step 6, you must divide by that expression in the parentheses (x^2 - xy). Since I just proved that it is going to equal 0, and since you can never divide by zero, then the problem thereafter really has no solution.

I'll be accepting my Nobel Prize now...

 

[Kripost]

0 = 0 + 0 + 0 + 0 + 0 + 0 +...
= (1 - 1) + (1 - 1) + (1 - 1) +...
= 1 - 1 + 1 - 1 + 1 - 1 +...
= 1 + ( -1 + 1) + ( -1 + 1) + ( -1 + 1) +...
= 1 + 0 + 0 + 0 +... = 1

Corrected form, rewrited using sigma,

0 = Σ 0
= Σ (1-1)
= 1-1+1-1+....-1
= 1+ (Σ (-1+1))- 1
= 0

The problem lies in paring +1 and -1.

 

[Kripost]

I'll be accepting my Nobel Prize now...

Unfortunately, like Computer Science, there is no Nobel Prize for Mathematics.
There is however, the Turing Prize for Computer Science, and Abel Prize for Methematics, both of which are a lot less well-known compared to Nobel Prizes.

 

[Bargainfluger]

Unfortunately, like Computer Science, there is no Nobel Prize for Mathematics.

NO! I REJECT YOUR REALITY! AHA HA HA HA!!!

sorry, too much time debating people about spirit worlds.

Anyway, who said anything about the math Nobel Prize? I was talking Literature, baby.

 

[HRE]

I'm very happy. I learned about this infinite series today in Calc, and I thought I'd put it here and see how many people would attack the philosophy before examining the math.

Thank you all for surprising me!

 

[funyun]

NM.

 

[Juvenal]

I'm very happy. I learned about this infinite series today in Calc, and I thought I'd put it here and see how many people would attack the philosophy before examining the math.

Thank you all for surprising me!

Life is full of surprises, and they're all good. True. There are only good times and good stories, if you remember that when the former fails, the latter is bound to be true.

Good luck on your studies. Seeing as you've yet to cover convergence tests, I'll answer my previous question here.

The first test for convergence is to see if the final term tends to zero.

In this case, that would be sufficient since the series is alternating, changing from positive to negative. This series has no limit, however, as it alternates between 1 and 0 when you consider the partials.

1 = 1
0 = 1 - 1
1 = 1 - 1 + 1
0 = 1 - 1 + 1 - 1
...



The other was a trick question. Girls ARE evil, thank god.

 

[Aeschylus]

For a start what's 0 + 0 + 0..... anyway? such infinite strings are not defined in fields. The concpet of the sum to infinity is precisley defined as the limit of the sequence of partial sums of a series. the infinite series 0 + 0 + 0..... is not equal to the infinite series 1 + (-1) + 1 + (-1)... even though the even partial sums of the latter series converge to 0.