At 12/21/09 04:59 PM, Deadclever23 wrote:
So logically 1/0*0 = 1 because the /0 and the *0 cancel each other out.
In the realm of non-real maths, anything that "logically" makes sense can sort of happen! Hurrah!
Although keep in mind that you can't say 1/0 equals 2/0 (because they don't). However, you can say that 2/0 = 2*(1/0) if you're choosing to define 1/0 as something.
Mathematically though, anything *0 is equal to 0.
In the real world, yes. But crazy things can happen when dealing with things which don't 'exist'!
For example, there is a mathematical rule that the (square root of one number) multiplied by (the square root of another number) is the square root of (both numbers multiplied together).
But when dealing with the imaginary [positive] square root of -1, i, this rule simply isn't true!
Remember that the rules you've learnt through schooling are true for the numbers you learned them with, but you can't say that the rule is true for everything until you've proven it free of logical inconsistencies with those numbers (and of course, the point you made in your post Deadclever was that there is a logical inconsistency with the non-real number 1/0 and the rule that multiplying by 0 always equals 0).
I've oversimplified and almost made a farce of mathematics, but it's vaguely easier to understand than Toast's complicated (yet beautiful) explanation.