Mathematics

[Steven Rogers]

Discuss anything about the wonderful world of mathematics here.

 

[Melix]

Okay. I learned some theorems in either elementary or middle school that said anything divided by 0 was undefined, 0 divided by anything was o, and anything divided by itself was one. So what's 0/0? And explain.

 

[Steven Rogers]

Let 0/0 = x. Multiply both sides by 0 to get 0/0 * 0 = x * 0. Simplifying, you end up with x * 0 = 0. Since any number times 0 equals 0, x, or 0/0, can be any number.

 

[Melix]

So it IS undefined. Thank you.

 

[Steven Rogers]

No, 0/0 can be 1, 50, 1337 or whatever real number you want. If by undefined you mean no definite solution then you'd be correct. But I prefer undefined to mean no solution.

 

[Mitheral]

The correct term is indeterminate.


Wikipedia has a fair explanation based on several concepts. (Undefined gets used a lot too.) The calculus approach yields the best explanation, though it is so abbreviated in the wiki that one may as well have used the phrase "just because I said so" as the logic.


Dividing by zero is referred to as an illegal operation for a reason. It introduces fallacies. (0/0 can also be called an illegal operation.) The 1=2 "proof" is a good example of how such an illegal operation can be abused.

 

[Steven Rogers]

Yes, indeterminate is the jargon that's meant to be used, but most people struggle with math, so I like to use layman's terms when teaching.


Speaking of dividing by zero fallacies...


x=y


x^2=xy


x^2-y^2=xy-y^2


(x+y)(x-y)=y(x-y)


x+y=y


x=0

 

[Mitheral]

Squaring and then dividing introduces fallacies regardless of whether zero is involved or not.


Start with X ... square it .. X^2 ... right?


sqrt(x^2) can be +X or -X.