Yes and no

PoisonCrystal is clearly breaking the rules in claiming that (a • b) + (c • d) = (a • c) + (b • d).

So in order to sort things up, I decided to share the true proof that 9 + 10 actually equals 21. My proof breaks no mathematical rules (I am a teacher, after all). Here is the complete proof:

Start with the axiom b - b = 0, where b is any number.

Based on this, we know that 25 - 25 = 30 - 30, since both sides represent b - b, which equals 0.

We know that 25 = 5 • 5, which means that the left side of the equation 25 - 25 equals (5 • 5) - (5 • 5)
We know that 30 = 6 • 5, which means that the right side of the equation 30 - 30 equals (6 • 5) - (6 • 5)

We now have the equation (5 • 5) - (5 • 5) = (6 • 5) - (6 • 5)

We can rewrite that as 5 • (5 - 5) = 6 • (5 - 5)

Divide by (5 - 5) on both sides to get 5 • (5 - 5) ÷ (5 - 5) = 6 • (5 - 5) ÷ (5 - 5)

Now we need another axiom c ÷ c = 1, where a is any number or expression.

If we treat (5 - 5) as c, then the (5 - 5) ÷ (5 - 5) factor on the left side equals 1.

We now have the equation 5 • 1 = 6 • (5 - 5) ÷ (5 - 5)

Since 5 • 1 = 5, the left side equals 5. We now have the equation 5 = 6 • (5 - 5) ÷ (5 - 5)

If we multiply both sides by 2, we get 2 • 5 = 2 • 6 • (5 - 5) ÷ (5 - 5)

Since 2 • 5 = 10, the left side equals 10. We now have the equation 10 = 2 • 6 • (5 - 5) ÷ (5 - 5)

We now have an expression for 10, which is 2 • 6 • (5 - 5) ÷ (5 - 5)

We can now go back to the original question 9 + 10. Since we just made an expression for 10, we can substitute 10 for that expression.

This means that 9 + 10 = 9 + 2 • 6 • (5 - 5) ÷ (5 - 5)

Since 9 = 3 • 3 and 6 = 2 • 3, we know that 9 + 2 • 6 • (5 - 5) ÷ (5 - 5) = 3 • 3 + 2 • 2 • 3 • (5 - 5) ÷ (5 - 5)

We can rewrite that as 3 • (3 + 2 • 2 • (5 - 5) ÷ (5 - 5))

Using the same axiom as before, c ÷ c = 1 and treating (5 - 5) as c, we can substitute (5 - 5) ÷ (5 - 5) for 1.

This means that 3 • (3 + 2 • 2 • (5 - 5) ÷ (5 - 5) = 3 • (3 + 2 • 2 • 1)

3 • (3 + 2 • 2 • 1) = 3 • (3 + 2 • 2)

3 • (3 + 2 • 2) = 3 • (3 + 4)

3 • (3 + 4) = 3 • 7

3 • 7 = 21

This proves that 9 + 10 = 21. If you find the flaw in my proof, you are worth an A in every math course below college.

ty i now know the truth:)

9 = 3 x 3 & 10 = 5 x 2. 3 (from 3x3) x 5 (from 5x2) = 15. 3 (from 3x3) X 2 (from 5x2) = 6
15 + 6 = 21 9 + 10 = 21

correct