Why 2 multiply 2 is equal 4?proof?

A quick proof, using The Field Axioms and definitions of 2 := 1+1, 3 := 2+1 and 4 := 3+1.

 

First by the distributive law for multiplication and addition.

[math]2 \times 2 = 2 \times (1+1) = (2\times 1) + (2 \times 1 )[/math]

 

Then with the identity property of unity

[math](2 \times 1) + (2 \times 1 ) = 2 + 2[/math]

 

Then with the associative property of addition

[math]2+2 = 2+ (1+1) = (2+1)+1 = 3 + 1 = 4[/math]

 

Q.E.D.

Any reason for such a question?

because ,Mathematical proof is one of the most important aspects of formal mathematics

unfortunately,they (turk students) didn’t really know how to apply the definition even though they can remember it.

only formula in turkey ...

but proof teaches us to think in very precise terms, which is a necessity in our field..