Tips and tricks!
Whenever you introduce a let statement in a proof (when you pick a variable), conclude the end of that margin with an existential.
Whenever you introduce a generic variable , conclude the end of that margin with a universal.
Brief review of floors:
- The floor of x is the largest integer that is less than or equal to x.
- The floor of x is not a variable. It is a function, and quantifiers only apply to variables, so you cannot use a quantifier directly on floor.
Definition of floor:
Assume y is an int. Then y is less than or equal to x. Among all ints that are less than or equal to x, y is the LARGEST.
Note that the symbolic definition of floor and the english definition of floor are equivalent; one is just simpler to parse as a native english speaker.
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