Dividing by zero

[Simsim]

Rational, this is exactly what I did. After that I showed how limits can give a definite solution for the operation 0/0 according to the state of the original fraction.

Take the fraction x*(x^2 + x + 5)/ x , when "x" approaches zero both the numerator and denominator approach zero and the total result would be 0/0 which is undefined. But while both the numerator and denominator are approaching zero the value of the total fraction is not undefined but it approaches a defined number which we can find. By omitting "x" in denominator with the "x" in the numerator we can reduce the fraction to this simpler formula: x^2+x+5

Thus when "x" approaches zero the total value, in this case, approaches 5

[little_monkey]

I'm not a math wiz. Why is it you can multiply by zero and get zero but you can't divide by zero?

Why doesn't 1/0 equal 0 but 1*0 does? Is there a reason or is it arbitrary?

A simple demonstration:

1/.1 = 10 = 10^1
1/.01 = 100 = 10^2
1/.001 = 100 = 10^3
.
.
1/.000001 = 1,000,000 = 10^6
.
.
.
1/.0000000001= 10,000,000,000 = 10^10
.
.
.

So as we divide by smaller and smaller dividors, we get a bigger and bigger answer. Now division by zero is not permitted but we can still symbolize it as:

Limit 1/n = ∞
as n → 0

Actually, this is the beginning of understanding calculus.

[Cyberman]

I was with you right up to the word "simple".

[bennyboy]

rather than using limits, you can use simple algebra to show why you can't divide by zero.
first, take expression like 1/0 and make it into an equation.
1/0=x
this equation would be equivalent to 1=0x
0x equals zero according to the multiplicative property of zero
so you get 1=0 which is simply not the case.

but what about 0/0?
this would be equivalent to 0=0x
which then gets you 0=0
so in the equation it works, so can it be done? well, not really. the problem is we have to solve for x, so then we have to answer what is x? well, x can literally be anything because anything times zero equals zero. so you pretty much get 0/0= all real numbers, which simply can't be the case for a division operation which is why it is instead expressed as undefined.

That's what I just said about 2 posts ago.

[little_monkey]

I was with you right up to the word "simple".

Taking limits is a concept invented in the 17th century. By now, it's really kindergarten stuff compared to complex integration and Residue theory.

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So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

That's totally wrong.

x*(x+1)/x approaches 1, if and only if x is NOT zero. At x=0, that algebraic fraction is infinite.

[Cyberman]

Well, as I said earlier, "to me mathematics is like giving birth: it looks painful and messy, I'll never completely understand it and I'd rather leave it to people who seem to know what they're doing anyway."

[Simsim]

So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

That's totally wrong.

x*(x+1)/x approaches 1, if and only if x is NOT zero. At x=0, that algebraic fraction is infinite.

Sorry, have you read what you quoted for me??

I didn't say that x can be 0

Again:

So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

And your expression is wrong. :

"" x*(x+1)/x approaches 1, if and only if x is NOT zero. At x=0, that algebraic fraction is infinite. ""

Wrong ! That means that whatever the value of x is, the value of the fraction approaches 1 as long as x doesn't equal zero ! That's obviously wrong !

And when x=0 the algebraic fraction will not be infinite as you said. It will be "undefined".

[little_monkey]

Sorry, have you read what you quoted for me??

I didn't say that x can be 0

Again:

[quote='Simsim' pid='514504' dateline='1380536264']

So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

I was referring to x*(x+1)/x = (x+1). Since you divided by x, that is only valid if and only if x is not equal to zero

[Cheerful Charlie]

I'm not a math wiz. Why is it you can multiply by zero and get zero but you can't divide by zero?

Why doesn't 1/0 equal 0 but 1*0 does? Is there a reason or is it arbitrary?

It is not arbitrary. It can lead to mathematical absurdities and errors. Such as 'proving' 1 = 2 and so on

http://en.wikipedia.org/wiki/Division_by_zero

[Chas]

http://en.wikipedia.org/wiki/Division_by_zero

Yeah. I've seen that but it doesn't make sense to me. Why not say 1*0 is undefined and 1/0=0?

Simple explanation.

Take 1/x
Make x smaller and smaller
1/x gets larger and larger
As x approaches 0, 1/x approaches infinity
So one can say that 1/0 is infinite, or undefined.

Take 1*x
Make x smaller and smaller
1*x gets smaller and smaller
As x approaches 0, 1*x approaches zero
So one sees that 1*0 is 0.

If you graph them (y= 1/x and y=1*x), it is immediately obvious.