Blog Post #68 - 1=2 How did that happen?

My elder son Arnav has taught my younger one Arush to answer 1 and 2 as the answer to any question .

I am still not sure how Arush knows when he is asked question it is a math question and as I mentioned earlier I have smart kid (this time I am referring to my  2 year old). 

Arnav would ask what is 1+1 Arush will say 2.Arnav will ask 1-1 Arush will say 2. 
I used to ask Arnav what is 0+0 and why is it not 2 zeros which means 2=0 .

Can these be proved mathemtically to show that Iam intelligent and so are my kids.

By the way QED at the end of any proof or theorem means quod erat demonstrandum which means  "which had to be demonstrated". I took pains to prove it - Hence proved is what it means. 

Sometime ago I was asked if I remember how 1=2 worked? Interesting. I thought I might have forgotten but apparently not.

Let                                                            a = b

Multiply by a on both sides                           a ² = ab

Subtract b2  from both sides                         a ²- b ² = ab- b ²

Rewrite a ²- b ² in i  in terms of (a-b)             (a-b)(a+b) = b(a-b)

Cancel out a-b from both sides                      a+b = b

Remember a=b so make a as b                      b+b = b

Now  do the simple addition                          2b = b

Divide by b                                                  2 = 1

QED

Now that we know we can make 2=1 why not also make 2=0 ?


Let                                                   a=b (why not ...let them be the same)
Square                                                          a ² = b ²
Take b ² from both sides                                  a ² - b ²=0 
Rewrite                                                         (a+b)(a-b) = 0
Divide by (a-b)                                               (a+b) = 0
So                                                                  2b = 0 
Divide by b on both sides                                  2 = 0

QED


What went wrong on both these proves?

Keep wondering
Sivakumar Manikanteswaran