Last Time | Next Time |
From our syllabus: "Companies have logos; you should have one, too! Your math logo will be something (like a family crest) that represents you. It will be created using elements from this course (or other mathematical elements of your own choosing). You will type up a one-page sheet, illustrating and explaining your choice. These will be presented the last day of the course."
(When is "infinite love" not enough?!)
Mobius bands have mobius bands inside them (just cut them into "thirds"). One could do this forever. Fractals are infinite, in a very real sense. Fibonacci numbers are infinite, as is the spiral (and, in the limit, when you get all the way to infinity... wait a minute.... then it becomes golden!).
Both of these images are by the astonishing artist M. C. Escher.
Eternity is tied up with the concept of infinity, frequently.
About another Newton (other than Sir Isaac): John Newton 1725-1807; ironically Newton was a slave trader (who ultimately saw the error of his ways).
Strogatz says that his objective is to "give you a glimpse of this paradise." (p. 253)
and if the
sets are finite, the proper subset is always
smaller....
but if the set is infinite, we may actually be able to
throw away elements of a set and not change the size of
the set!
There are infinitely many sizes of infinity. It turns out that the power set of a set is always of larger cardinality than the set itself. Thus every infinite set is smaller than its power set, which is an infinite set, which is smaller than its power set, etc....