I'm in geometry, soo imma prove you're right with the indirect method (ax. = axiom):

0 ÷ 0 = 1 <=== Suspect this is true

( 0 ÷ 0 ) - 1 = 0 (Subtraction ax.)

1 - 1 = 0 0 ÷ 0 = 1 (Substitution ax.)

0 = 0 This is true (identity)

no contradiction, thus the problem is satisfied. boom