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lect06a
functions
Functions:
f : A -> B
domain, codomain.
Example:
string-length
[Note: can't include 'null' as a String and still have it be a function]
favorite-color : Person -> Color
[Note: we assume everybody has *some* fave color, and it doesn't change over time.]
Integer.toString : int -> String
Puppy.toString : Puppy -> String
(the default, vs a version we write.)
nextInt : java.util.Random -> int
No: Random rng = new Random();
rng.nextInt() == rng.nextInt() // probably false.
sqrt: is this really a function?
New set notation: intervals.
sqrt: [0,+Infinity) -> [0,+Infinity)
max: RxR -> R
or consider generalizing: max set-of-R -> R
new notation: P(S).
Def'n of function; the *graph* of a function.
N.B. Constant functions.
N.B. The identity function.
functions on numbers: increasing; non-decreasing.
Two particular functions: ceiling, floor.
def'n: 1-1, onto.
(For 1-1: give both def'n and phrase as contrapositive)
composing functions
Inverse.
Function spaces.
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Sums
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Cardinality:
N vs Sigma*; N vs Primes; N vs Odd;
N vs Java;
N vs NxN
N vs R
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