1. Revision of topics/definitions
Nicholas Lawrance | ICRA 2011

2. Injective transformations
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3. Surjective transformations
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4. Bijective transformations
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5. Sequences
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6. Sequences N = {1, 2, 3, ...} is countably infinite
The rational numbers Q are countable, the real numbers R are not
Examples
Can also have a finite index set, and a subset of the index results in a family of elements
Nicholas Lawrance | ICRA 2011

7. Supremum and Infimum
Easy to think of as maximum and minimum, but not strictly correct. They are the bounds but do not have to exist in the set
A = {-1, 0, 1} sup(A) = 1 inf(A) = -1
B = {n-1: n = [1, 2, 3, ...]} sup(B) = 1 inf(B) = 0
Nicholas Lawrance | ICRA 2011

8. lp - norms For an n-dimensional space
2-dimensional Euclidean space unit spheres for a range of p values
Nicholas Lawrance | ICRA 2011

9. Nicholas Lawrance | ICRA 2011