Transcript Slide 1

Young man, in
mathematics you don't
understand things. You
just get used to them.
— John von Neumann
Orders of Infinity
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If each element in red set can
be paired (1-to-1) with an
element in the blue set, sets
have same cardinality.
Smallest infinite set is the set of
natural numbers N = {1,2,3…},
said to be a countable infinity,
cardinal number 0.
Countable sets: N, Z, Q
Next cardinal number is c, the
cardinality of the continuum.
Sets with cardinality c: [0,1], R,
C, Rn
 Lines, surfaces, volumes,… have
same “number” of points!