1+1=1???

I know...it sounds ridiculous right? Well...I refer that equation as "ajaran sesat" by my Calculus II lecturer.

One simple example: 1 Group of sheep, add with 1 Group of sheep. What do you get if you add them together? 1 Group of sheep. (although it's a bigger group...but it's still 1 group right?)

He then showed us this equation:

x=y

Nothing wrong right? Now we go to the next step:

x(x)=yx

x^2=xy

We multiply both side with x. This would be sensible right even if you are still PMR level..i think.

Anyway, we go to the next part, we reduce both side with y^2

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

We still obeyed the algebraic rules, add/subtract/mutltiply/divide/play football/learn how to fly kite on BOTH SIDES.

So...we factorize!

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

Can we divide both side with a same denominator? Sure! (x-y)!! 8D Then we get...

x+y=y

That would be the end product. Now let's recap the first part (x=y)

Since x=y, then if x=1, hence, y=1. You substitute both unknows...

1+1=1

I know, it sounds unreasonable, and it actually is in some sense. He showed us the flaw with that theory if we use 0 and the application of limits and infinity. But that's the boring part...so let's just savour the screwed-up system that is Calculus II: Improper Integrals.