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hi i'm rob welcome to math antics by now you probably know that math involves a lot of calculations using arithmetic but math is about more than just calculations in fact one important type of math that sometimes gets overlooked involves number patterns now when you hear the word pattern you might think of a shirt yep and i'll bet you wish you had some fine threads like these don't you oh actually i'm good with this shirt thanks i get it not everyone can pull off a look this rad that's true of course the reason you might think of a shirt is because the word pattern often describes repeating images or objects like if i show you this pattern dog cat bird dog cat blank what animal do you think should fill in the blank to complete the pattern a bunny why would you think it was a bunny well because i like bunnies well well it's not a bunny it's a bird see how the pattern repeats dog cat bird dog cat bird well mr whiskers and i prefer the pattern dog cat bunny dog cat bunny anyway number patterns can be formed by repeating numbers like this 147147 notice how the order of the pattern really matters if you switch any of the numbers it becomes a different pattern in math when you have a set of numbers or elements where the order matters it's called a sequence for example the sequence 1 2 3 is different than the sequence 3 2 1 even though they each contain the same set of numbers and in math the word set refers to a group of numbers or elements where the order doesn't matter and where any duplicates are left out for example if you add the sequence 1 2 3 three two one the set of numbers in that sequence is just one two three even though each number occurred twice in the sequence both sets and sequences use the same notation in math each number or element is separated by a comma and the whole group is put inside curly braces like this some sequences of numbers repeat like the sequence 0 1 0 1 0 1 but some don't repeat like the sequence 1 2 three four five six but think about both of those sequences for a second right now each of them contains a limited or finite number of elements they each have six but each of these sequences could be continued forever if we wanted to we could just keep repeating 0 1 0 1 forever or we could just keep counting 7 8 9 10 forever 2. in other words sequences can be finite or they can be infinite if a sequence or set is finite it means that you can say there are a specific number of elements in it like 6 or 20 or a million but when something is infinite it means that no matter how much time...