Mathematical Notation Flashcards
What does the symbol => mean?
The symbol => means ‘leads to’ or ‘implies’
What does the symbol <= mean?
The symbol <= means ‘is implied by’ or ‘follows from’
What does the symbol <=> mean?
The symbol <=> means ‘it implies and is implied by’ or ‘is equivalent to’
What does a sufficient condition mean?
If A is sufficient for B, then A => B
If A is true B is also true
B is true does not mean A is true
What does a necessary condition mean?
If A is necessary for B, then A <= B
B cannot be true unless A is true
A can be true even if B is not true
What is the converse of a theorem?
The converse is the the opposite of a theorem
What is conjecture?
A conjecture is a mathematical statement that has yet to be proven
What is a theorem?
A theorem is a mathematical statement that has been proven
What must a proof include?
Show all assumptions you are using
Have a clear sequential list of steps that logically follows
Must cover possible cases
Make a concluding statement
What is proof by deduction?
A proof that consists of using known theorems to prove a given statement is always true
What is proof by exhaustion?
Testing every case
