# 1.N equals N plus one joke

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

# 2.Three is equal to four joke

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

# 3.All numbers are equal joke

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.

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