0*0 != 0

[conkermaniac]

Well, I was playing around with zero and exponents when I figured out a way to prove that 0*0 != 0. Knowing that this cannot be possible, I was wondering if you guys could help?

Let us assume that 0*0 = 0.
Therefore, 0² = 0.

a^(-m) = 1/(a^m)
0ˉ² = 1/(0²)
0ˉ² = 1/0 //substitution
Therefore, 0ˉ² is undefined.

0² = 1/(0ˉ²)
Since we proved above that (0ˉ²) is undefined, 0² cannot be solved.

So where did I go wrong? :confused:

[is0lized]

Eh? :confused:

[Kaliber]

You seriously have too much time on your hands

[conkermaniac]

Originally posted by Kaliber
You seriously have too much time on your hands

Huh? It only took me 10 minutes of experimenting to come up with this. :confused:

[CareBear]

Originally posted by conkermaniac
So where did I go wrong? :confused:



*snip*
0ˉ² = 1/0 //substitution

0² = 1/(0ˉ²)
0² = 1/[undefined] <-- wrong

should be:
0² = 1/(1/0) = (0.1)/1 = 0(1/1) = 0.1 = 0

[tandoc]

we'll just say 2+2=5

+4 = +5
+4 - +4.5 = +5 - +4.5
+0.5 = -0.5
sqaure both sides by itself[+ x + = + ] [- x - = +]

0.25 = 0.25

where be the error?

0.5 = -0.5

is where the 'real' error is - has to do with the signs - u can only add 1 sign to each side.

which signs do u put?

[on topic]
i have no idea what conker is on about...

[tandoc]

what he is trying to say - is 1 + 1 = window!!!

[n7of9]

tandoc, you just made by whole damn day

ROTFLMAO

[conkermaniac]

Originally posted by CareBear
*snip*
0ˉ² = 1/0 //substitution

0² = 1/(0ˉ²)
0² = 1/[undefined] <-- wrong

should be:
0² = 1/(1/0) = (0.1)/1 = 0(1/1) = 0.1 = 0

CB, I know that what you said can be done, but 0ˉ² does equal "undefined", and therefore, the problem can't be solved. :)

LOL at tandoc! ROTFLMAO

[CareBear]

for 0^-2:
lim x^(-2) = (1/0²) = infinity squared = infinity
x-> 0

for 1/(x^-2):
lim 1/x = 0
x -> infinity

so 0² = 0

It works out fine... you're just trying to get people confused :p

[CareBear]

btw:
a^(-m) = 1/(a^m) is for any a != 0
The rule doesn't apply for zero.

It comes from:

a^(+m-m) = a^0 = 1
but when a= 0: a^0 = 1 = 0^0 and 0^0 is undefined so invalid.

[conkermaniac]

Thanks, I understand now! ;)

[CareBear]

*waits patiently for any possible reward* :D

[Ben]

All this math makes my brain hurt. :chinese2:

No, really, you people seriously have too much time and too little to do... :p

[CareBear]

Originally posted by Ben
No, really, you people seriously have too much time and too little to do... :p I have plenty to do, I'm just very good at procrastinating and finding excuses to not get it done ;)

[Ben]

Originally posted by CareBear
I have plenty to do, I'm just very good at procrastinating and finding excuses to not get it done ;)
"I wanted to go to Procrastinators Anonymous, but I kept putting it off" :p I don't remember where I found that quote...

[Blank Verse]

I just read a math thread. I feel so dirty.

[Wojtek]

Originally posted by conkermaniac
Well, I was playing around with zero and exponents when I figured out a way to prove that 0*0 != 0.

What exactly " != " is ??

[Ben]

Originally posted by Wojtek
What exactly " != " is ??
'the stuff on the right is not equal to the stuff on the left' :)

[tandoc]

NO!!! - YOUR MOM!

[Bruce]

Originally posted by tandoc
NO!!! - YOUR MOM! No; subtract your mom. :confused2

[EpidemiK]

Originally posted by Bruce
No; subtract your mom. :confused2

No its:

No; subtract your mom.
-------------------------------
; subtract your mom.

Which then equals No. :p

[EDIT]
(It's supposed to be a fraction :cool: )

[Hoth]

They just invent rules arbitrarily to make things work out the way they like. 0*0 = 0 because someone wanted it to enough that they wrote it into the system.

They're doing this sort of thing all the time. Calculus, for example, rests on the lie that infinite series can have a finite sum. That's obviously false... if you're adding an infinite number of positive quantities you logically have to get infinity. What they wrongly call convergent series are just infinite series that get there too slowly for us to imagine.

Proof that 0=1 (http://www.csus.edu/indiv/d/dowdenb/misc/god.htm)

[conkermaniac]

Oooh...I made one of those 0=1 proofs too! ;)

Take a look (the problem here should be obvious):

1/(1+2+3+...) = 0 (given)
[1+2+3+...][1/(1+2+3+...)] = [1+2+3+...][0] (multiply both sides by [1+2+3+...])
(1+2+3+...)/(1+2+3+...) = 0
1 = 0

You could also write it a different way:

1/�‡ = 0
(�‡)(1/�‡) = (�‡)0
�‡/�‡ = 0
1 = 0

:D

[CareBear]

Originally posted by Hoth
Calculus, for example, rests on the lie that infinite series can have a finite sum. That's obviously false
The series:
u(n) = x/2 + x/4 + ... + x/(2^n)
which converges to x when n goes to inifinity and this certainly holds true in real life.

Try travelling a distance by walking half the remaining distance each time and then resting. No matter how hard you try you will get where you're going eventually. It won't take you an infinite amount of time :).

& 1/(1+2+3+...) = 0 (given) <- nah ah! you can only calculate the limit of the left side which will reach 1/infinity = 0. Without lim(...) around it the value is undefined. You're "cheating" again :p

[Hoth]

Originally posted by CareBear
Try travelling a distance by walking half the remaining distance each time and then resting. No matter how hard you try you will get where you're going eventually. It won't take you an infinite amount of time :).

Actually, going half the remaining distance each time I'd never get there, I'd die of old age. If you actually try it, you'll be going a nanometer and then resting before going half a nanometer... which will certainly leave you dying of old age before you get where you want to go. Now, perhaps there comes a point at a small enough scale where going half the distance no longer makes sense and you simply can't do it (where the concept of space no longer applies properly... certainly at the Planck length we could say that)... but if you could, it would take an infinite amount of time. As I said, simply try it in practice and you'll notice just how long it's taking you. Zeno was right. (Where Zeno was wrong is the presumption that it's possible to go only half the distance all the way down... the presumption that the macroscopic concept of continutity of movement need apply all the way down.)

[conkermaniac]

Originally posted by Hoth
Actually, going half the remaining distance each time I'd never get there, I'd die of old age. If you actually try it, you'll be going a nanometer and then resting before going half a nanometer... which will certainly leave you dying of old age before you get where you want to go. Now, perhaps there comes a point at a small enough scale where going half the distance no longer makes sense and you simply can't do it (where the concept of space no longer applies properly... certainly at the Planck length we could say that)... but if you could, it would take an infinite amount of time. As I said, simply try it in practice and you'll notice just how long it's taking you. Zeno was right. (Where Zeno was wrong is the presumption that it's possible to go only half the distance all the way down... the presumption that the macroscopic concept of continutity of movement need apply all the way down.)

Yes, I totally agree. While it is physically impossible for us as humans to travel half a micrometer, theoretically it is possible.

[CareBear]

Originally posted by conkermaniac
Yes, I totally agree. While it is physically impossible for us as humans to travel half a micrometer, theoretically it is possible. except most of our everyday life is in the physical world :).

[Hoth]

It is physically impossible for us to travel only half a micrometer. Of course that doesn't mean we can't pass through such a distance, it just means we can't be sure that "passing through" can be interpreted in quite the same way at that level as we interpret it when we pass through a macroscopic area. That's why we should no longer expect the intuition "to travel somewhere you have to first cover half the distance, and half of that, etc." (Zeno's paradox, in which Zeno says this proves motion is impossible) to hold below a certain level. To look at our every day experience and say "it must work like this all the way down" is to presume without evidence. Space can't be understood in the same way at the quantum level. For example, it's physically impossible for an electron to travel less than a complete energy level.