You know that Samuel Clemens is Mark Twain.I find it hard to accept what's I'm going to say !
if A=B , is it the same to say B=A? if it's, then why? what's confusing me A=B isn't in writings the same B=A so how we determined that A=B is the same as B=A!!!!!
Since another question hints that you know something about computer programming, it may be worth pointing out that "=" can be used in different ways. Sometimes order doesn't matter, sometimes it does.if A=B , is it the same to say B=A? if it's, then why? what's confusing me A=B isn't in writings the same B=A so how we determined that A=B is the same as B=A!!!!!
I know it's equal, but who said we just care on equal? maybe also on the order of writing the elements of two sides of equation .. who said not?!
I understand that, but I mean why we are approximating Y and Z , what about X .. isn't he affect the approximation of Y relative to Z? I mean if it was given Y+Z then I accept the approximation if Y smaller than Z then YYour second question:
Instead of saying that "Y is regardless to Z", I think what you mean is that "Y is relatively small compared to Z".
For example if Y = 0.0001 and Z = 100000 and X is whatever you like
X(Y+Z) = X(0.0001 + 100000) is approximately X*100000 ie X*Z, not exactly of course but approximately.
I almost got your point ! but still confused really about how it's not affected .. I'm not totally convinced !No, if Y and Z are specific numbers then "approximation of Y relative to Z" is not "affected" by any other number. We can asses the relative sizes of Y and Z by "Y/Z" or "Z/Y". That has nothing to do with any other number, "X". And the fact that it is "correct to do first approximation to the first term "(Y+Z)" and then multiply it by X" comes from the meaning of parentheses in mathematics: X(Y+ Z) means "first do Y+ Z, then multiply the result by X.
If you want to do it this way as well, then...
X(Y + Z) = XY + XZ. Since Y is small compared to Z then XY will be small compared to XZ. If you don't see this directly, put some numbers in like Harry_the_cat suggested in post 4.
Actually, the approximation takes no time at all; it's just ignoring the Y, right?So my question is how to do that directly ....? it takes me a lot of time to understand and do the approximation, in that case what can I do?
but lets assume you have EXP(LOG(EXP(LOG(EXP(X-Y))))) and X is neglected relative to Y, so my problem how do I do mental Effort on EXP(LOG(EXP(LOG(EXP(x-y))))))) i'M NOT robot ..what you're talking about ...It requires mental effort, Ryan.
Are you willing to do some work?
Both methods have been given to you.So my question is how to do that directly ....? it takes me alot of time to understand and do the approximation , in that case what can I do?