A proof is a watertight argument: a chain of justified steps that starts from things already known and ends at the statement you want to establish.
Checking that a claim works for a few numbers is not a proof, because a later case you did not try might still break it.
A deductive proof settles every case at once by arguing with symbols rather than examples.
Two symbols matter here. The equals sign $=$ links expressions that are equal for particular values, which you find by solving.
The identity sign $\equiv$ links expressions equal for all values, so there is nothing to solve; the two sides are always the same thing written differently.
Unlock the rest of this chapter with a free account
