SP20:Lecture 14 prep
I will use the following notation:
We often want to prove that there exists a sequence of values , all in , satisfying some property. Formally, we would say "there exists and values such that ".
This takes a lot of writing, and also requires us to introduce the variable there exists such that ".(which often just adds complexity). So, we will abbreviate this to "
We will also abbreviate sums and products of all the values:Note: there is ambiguity in this notation about whether we allow denotes the sum of the and denotes their product. We won't worry too much about the indices; unless otherwise specified, we just mean add (or multiply) all of them. finite or infinite sequences. I will only use this notation for finite sequences.
Come to lecture knowing the following definitions and how they relate to your existing notion of quotient and remainder: