8 = 2^3
ln(8) = ln(2)*3
from here, we can write:
ln(8)/ln(2) = 3

a^b = c^d
ln(a)*b = ln(c)*d

x can be any number than can be LN'd

ln(1) = ln(x)*0
1=x^0

ln(x) = ln(x)*1
x=x^1

0=0^x
ln(0)=ln(0)*x
are powers of 0 legal?
maybe not
0*0=0
cannot mutiply zero... zero cannot be mutiplied, can it? so how can you mutiply zero with zero?
zero is a mutiple of what? what is a mutiple of zero?

ln(1)*x = ln(1)
1=1^x
however, others would start with 1n(1)/1n(1) = x
you cannot divide by zero... but wait!
0*x=0
remember, zero cannot be mutiplied
0+0...=0
0+0+0...=0
0+0+0+0...=0
0+0+0+0+0...=0

0*x is a "false" expression which really equals 0.

0*0 = 0+0
0*0*0 = 0+0+0
0*0 = 0+0

??? you cannot mutiply or divide zero into something else. you do not have to mutiply zero with zero because it equals zero.

the following is wrong
0*x=0
x=0/0
wrong!

cannot mutiply zero
0*x >> false!
0 >> true!
x-x >>> true!

false does not equal true:
0*x=0
wrong!
x-x=0
correct!

or does it?
is 0/0 false?
many assume it is, but if it wasn't, then

ln(1)=ln(1)*x
so
1=1^x
would be true

if 0/0 is false
then so is 1^x

but isn't 1^x ok? if it was, then 0/0 would be too.

say that 1^x is false
1 >> true
1^x >> false

this is like saying
1^x >> false
1^(1/0) >> false

neither is correct

1*1 = 1+0
1*1*1 = 1+0+0

1/1 = 1+0+0
1/1/1 = 1+0

0*0=0+0
0*0*0=0+0+0
0*0=0+0

can you really divide and mutiply 0?
0 is a mutiple of what? what are the factors of 0?
what is a mutiple of 0? what number has zero as a factor?
can zero be a factor of a number?
if not, then you cannot mutiply a number with zero to get a number.

how many factors are there for zero, if zero can be a factor?
the factor cannot be zero, if zero is not a factor of the numbers 2, 3, 4, etc.
does zero have any factors at all if there is no mutiple of zero?

cannot mutiply and divide zero? your answers please.

remember, it is possible to do x-x=0 and x-1.5x=-.5x and such... so it's still possible to do all sorts of math without having to mutiply by 0.

but does x*0 reflect the logic and structure of the universe?

captialism.... is it because of the concept of *0 that debt has not been eliminated?
money doesn't have to represent the worth of our work, but is that fair?

therefore, i propose that a new understanding of the workings and nature of zero will improve the economy and elimnate debt.

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

What a long post. Here's a short answer.

Yes, you can multiply by zero. The answer is always zero.

No, you cannot divide by zero. It's meaningless.

Yes it does. You have three pairs of shoes. How many shoes do you have? 3*2.
Now, how many shoes do you have if you have no pairs of shoes?

Could you lend me a hundred while I think about this?

x+0=x
x-0=x
x×0=0
x÷0=infinite
x^0=1

There's nothing more to be said on the matter.

Except your fourth one is usually considered false (instead, it's undefined), and the last one is sometimes undefined.

This is somewhere in the swamplands where philosophy and mathematics meet, but I alwys thought that "x/0=infinite" isn't really true. x/0 simply does not have a meaningful answer. It is true however, that

lim(x/y) = infinite
y -> 0

That's my understanding anyway, and I may well be wrong. Either way, it shows that you don't need a complicated equation to make your eyes spin round and your head hurt.

Well, if you want to get pedantic. I have enough of limits after a couple of my friends were discussing them while we were queuing for a ride at Alton Towers.

Warning: The original post should have been made in BABBling!

Yes, but logarithms are not-so-legal.

It can, usually.

There's nothing false about it. Zero can be multiplied as many times as you like.

?!

Not false, but meaningless.

And it is, usually.

All numbers are factors of zero.

Zero.

Zero.

See above.

I believe so.

You should ask that question in a forum devoted to economics.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

lol :P

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

Me? I thought you... h*ck, show me the p*b.

That was my first reaction, as well. But I had some time to kill.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

x/0 = undefined
x = undefined*0
x = x/0*0 = 0/0
0/0 = undefined
x = undefined
x/0=x

would you agree that x another way to say undefined?

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

No, it's another way of saying 'arbitrary number'.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

undefined is also arbitrary... x and undefined can both be described as "arbitrary".

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

No, they mean different things in mathematics.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

ok.

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

x/0 = undefined
0^0 = undefined

if
Step 2: x/0 = 0^0
Step 1: x = 0^1

x=0

where
x/0 = undefined

what can x equal?

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

It's a subtle distinction, but an important one. Talk to your local math teacher/professor for more details.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Pointers for those insterested:

o Multiplication: http://mathworld.wolfram.com/Multiplication.html
o Division: http://mathworld.wolfram.com/Division.html
o Zero: http://mathworld.wolfram.com/Zero.html
o Division by Zero: http://mathworld.wolfram.com/DivisionbyZero.html

edit: added a few

I was wondering if something like this would come up sooner or later! This is a site that I stumbled across a few months back regarding "division by zero".

http://members.lycos.co.uk/zerobyzero/index.html

This person actually does answer your email messages, but if you disagree with him (as I did) be prepared to be told that your mathematical ability is of kindergarten standard!

__________________
The plural of "anecdote" is not "data".

Actually, this isn't correct. x/0 is undefined; 0^0 is undefined. They do not equal undefined. They don't equal anything.

There you have it! The Math of the 21st Century!
Glad that someone there did it before I would need to.

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

well i know that "doesn't not make sense" does not equal anything.

the meaning of the word "is" is this
the meaning of the word "is" equals this:

two plus two is four
two plus two equals four

if 2 divided by 0 does not equal undefined
then 2 divided by 0 is not undefined....

but that is essentially wrong (hopefully we remember) that 2 divided by 0 is undefined.

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

'Undefined' is a property possessed by the expression x/0, not the value of the expression.

'The grass is green' does not mean 'the grass equals green'

this is why 21/0 does not equal 0
21/0 = 0
21 = 0*0
WRONG


now, this is why 2/0 does equal 0!
21 \ 0 = 0
(21*0) \ 0 = (0*0)
0 \ 0 = 0
0 = 0 * 0

NUFF said.
http://members.lycos.co.uk/zerobyzero/index.html

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

How are you seeing that that says 2/0 equals 0?

And 21/0 is not 0.

this is because:

however. empricially, say we have 10 ounce pie / 5 pieces = 2 ounce-pie-pieces
10/0 ... a 10 ounce pie per 0 pieces? no!
0/0 ... 0 pieces / 0 pie = 0 ounces

therefore the steps that this:
21 \ 0 = 0 >> 21 ounces per pie... but never mind, (\) no pieces, therefore (=) no ounces of pie
(21*0) \ 0 = (0*0) >> no (0) (*) 21-ounce pie per (\) 0 pieces (=) 0 ounces for (*) 0 pie
0 \ 0 = 0 >> 0 ounces per (\) 0 pie (=) 0 ounces of pie.
0 = 0 * 0 >> 0 ounces for (=) 0 pie with (*) 0 ounces each

http://members.lycos.co.uk/zerobyzero/index.html

don't mind my spelling mistakes.

__________________
cause of event ≠ explanation
My Cyclical Multiverse Hypothesis

I'm not really convinced, especially since you're conclusions don't follow logically from your premises.

Just my 1/50th of a dollar, from a guy who graded his mom's Algebra 1 tests for years:

Once you each a step where you find yourself dividing by zero, you're stuck. Since the operation of division by zero is undefined, further algebraic manipulation is pointless. Any further results will also be undefined, and meaningless.

__________________
I am a doctor, but I don't play one on TV.

Interestingly, this problem of division by zero is similar to the bet Hawking just lost.

Mathematically you can have a singularity: a point (zero) that essentially allows only one-way transformation of information. You can multiply by zero, but attempt to divide, and given that 0 has infinite factors, it is impossible to reach any conclusion, even infinity - as that is still more definite than a divide by zero operation will allow. It is a hopeless case, as 0/0 = infinity is just as valid as saying 0/0 = 0, so 0 = infinity?

Sorry, it's meaningless.

It took me only one paragraph to find some nonsense: :roll:

When mathematicians first started treating zero as number, the world was already well known not to be flat.

Just so you have an idea of what is wrong in that website, the following is from the preface:

Wrong!

When you do not wish to divide, you pick 1 as the divisor! Anyone who's gone to highschool should know this. Even earlier than that.

'Nuff said, indeed.

kmarinas86, take a chance in your life, and talk to a mathematician or a math teacher. What have you got to lose?

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.