Proving Any Two different Numbers are Equal — Paradoxical Solution

Of course we all know, that a number is equal to itself or something evaluated to represent the same number. E.g 1 = 1 or 1 = 3–2 . So what if we are taking 2 totally different numbers and try to prove both are mathematically equal ??Yeah..!!

Before that let’s see what a Paradox is. Most of the intelligent people like you are already well aware of what a paradox is. Still, as this topic writer I would like to throw lights on it. Paradox is facts or situations that neither you can accept nor you can deny logically. You cannot prove it at the same time you cannot disprove it too ! Confusions with clarity in it. A famous statement paradox made by one of the Greatest scholar ‘Socrates is

“I know one thing . That I know nothing”

Consider this famous philosophical quote. Quote itself has two contradicting statements. If you believe in first statement , the second statement is false and vice versa. Collectively both makes sense and no sense too . Yeah that’s the Paradoxical situation. Now lets come back to our topic.

am gonna prove two different numbers are mathematically equal. Let’s take this two numbers 103,97 and prove both are equal

So.. To Prove 103 = 97

Every mathematical solution builder has the first step of assuming things , later we got to prove it. So I assume two variables ‘a’,’b’ are equal

step 1 : Assuming a = b ==> Equation 1

step 2 : Multiply the equation 1 with ‘6’ on both sides which makes

6 x ( a = b ) ==> 6a = 6b ==> Equation 2

step 3 : In equation 2, Can we replace the ‘6’ with something relevant to our problem ??? yeah.. let’s replace 6 = (103–97 ) in equation 2

(103–97) a = (103–97) b ==> Equation 3

step 4 : Now as any mathematical guy, you can get it what we gonna do next.

103a-97a = 103b-97b ==> Equation 4

step 5 : Now we re arrange the Equation 4 , with having same Numbers on same side

103a-103b = 97a-97b ==> Equation 5

step 6 : Take the common factor on both sides in Equation 5

103(a-b) = 97(a-b) ==> Equation 6

step 7: Obvious.. Isn’t it ?? Cancelling common things on both sides in equation 6.

103 = 97 ( After crossing out (a-b) on both sides ) == Equation 7

Wait.. What ??? Isn’t this what we tried to prove ?? Really 103 = 97 ?? But here we have solved step by step and proved too. Can you disprove it or say what we did isn’t mathematically logical ? Yep. Paradoxical it is. A mathematical paradoxical way to prove two different numbers to be equal. By this time you could’ve figured out what we did, still I’m not revealing. Felt silly , bored or had any expression? express it in comments !!