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In this sequence of segments,
we review some mathematical

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background that will be
useful at various

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places in this course.

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Most of what is covered, with
the exception of the last

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segment, is material that you
may have seen before.

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But this could still be an
opportunity to refresh some of

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these concepts.

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I should say that
this is intended

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to be just a refresher.

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Our coverage is not going to
be complete in any sense.

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What we will talk about is
sets, various definitions

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related to sets, and some basic
properties, including De

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Morgan's laws.

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We will talk about what a
sequence is and what it means

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for a sequence to converge
to something.

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We will talk about
infinite series.

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And as an example, we will look
at the geometric series.

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Then we will talk about some
subtleties that arise when you

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have sums of terms that are
indexed with multiple indices.

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And finally, probably the most
sophisticated part, will be a

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discussion of countable versus
uncountable sets.

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Countable sets are like
the integers.

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Uncountable sets are
like the real line.

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And they're fundamentally
different.

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And this fundamental difference
reflects itself

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into fundamentally different
probabilistic models--

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models that involve discrete
experiments and outcomes

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versus models that involve
continuous outcomes.