Maths Fun

Three is equal to four 

Theorem: 3=4
Proof:

Suppose:
a + b = c

This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c

After reorganizing:
4a + 4b - 4c = 3a + 3b - 3c

Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)

Remove the same term left and right:
4 = 3 

Dollars equal ten cents 

Theorem: 1$ = 10 cent
Proof:
We know that $1 = 100 cents
Divide both sides by 100
$ 1/100 = 100/100 cents
=> $ 1/100 = 1 cent
Take square root both side
=> squr($1/100) = squr (1 cent)
=> $ 1/10 = 1 cent 
Multiply both side by 10
=> $1 = 10 cent

One + one are two 

Theorem: 1 + 1 = 2
Proof:
n(2n - 2) = n(2n - 2)
n(2n - 2) - n(2n - 2) = 0
(n - n)(2n - 2) = 0
2n(n - n) - 2(n - n) = 0
2n - 2 = 0
2n = 2
n + n = 2
or setting n = 1
1 + 1 = 2

ll numbers are equal 

Theorem: All numbers are equal.
Proof: Choose arbitrary a and b, and let t = a + b. Then


a + b = t
(a + b)(a - b) = t(a - b)
a^2 - b^2 = ta - tb
a^2 - ta = b^2 - tb
a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
(a - t/2)^2 = (b - t/2)^2
a - t/2 = b - t/2
a = b


So all numbers are the same, and math is pointless.

Log negative one zero 

Theorem: log(-1) = 0
Proof:
a. log[(-1)^2] = 2 * log(-1) 

On the other hand:
b. log[(-1)^2] = log(1) = 0


Combining a) and b) gives:
2* log(-1) = 0
Divide both sides by 2:
log(-1) = 0

N equals N plus one

Theorem: n=n+1

Proof:
(n+1)^2 = n^2 + 2*n + 1

Bring 2n+1 to the left:
(n+1)^2 - (2n+1) = n^2

Substract n(2n+1) from both sides and factoring, we have:
(n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)

Adding 1/4(2n+1)^2 to both sides yields:
(n+1)^2 - (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 - n(2n+1) + 1/4(2n+1)^2

This may be written:
[ (n+1) - 1/2(2n+1) ]^2 = [ n - 1/2(2n+1) ]^2

Taking the square roots of both sides:
(n+1) - 1/2(2n+1) = n - 1/2(2n+1)

Add 1/2(2n+1) to both sides:
n+1 = n