Strict logical proofs by deduction, including parity arguments with even and odd integers written as n=2k and n=2k+1, and direct proofs that two expressions are equivalent by showing
A proof is a strict logical argument that demonstrates with mathematical certainty that a statement is true.
For SL students, these proofs will be in the form
Prove that
where ≡ means equivalent, i.e. equal for ALL variables in the expression, not just some specific intersections.
We use LHS (left-hand side) and RHS (right-hand side) as an abbreviation for one side of the equivalence.
The parity of an integer describes whether or not it is divisible by 2. We say that
In general, even numbers take the form n=2k, and odd numbers take the form n=2k+1 for some k∈Z.
Nice work completing Proof by deduction, here's a quick recap of what we covered:
Exercises checked off
Strict logical proofs by deduction, including parity arguments with even and odd integers written as n=2k and n=2k+1, and direct proofs that two expressions are equivalent by showing
A proof is a strict logical argument that demonstrates with mathematical certainty that a statement is true.
For SL students, these proofs will be in the form
Prove that
where ≡ means equivalent, i.e. equal for ALL variables in the expression, not just some specific intersections.
We use LHS (left-hand side) and RHS (right-hand side) as an abbreviation for one side of the equivalence.
The parity of an integer describes whether or not it is divisible by 2. We say that
In general, even numbers take the form n=2k, and odd numbers take the form n=2k+1 for some k∈Z.
Nice work completing Proof by deduction, here's a quick recap of what we covered:
Exercises checked off