Theorem on formal functions
A formal function is like a special way of writing down a bunch of numbers with an infinite amount of terms. Sometimes we want to do math with these formal functions, but we have to be careful because they don't always behave like regular numbers do.
The theorem on formal functions tells us that if we have two formal functions that are equal for all except a finite number of terms, then they are actually the same formal function. This means that we can do operations on these formal functions even if they look a little different from each other.
Think of it like having two sets of legos that look slightly different, but have all the same pieces except for one or two. Even though they may look a little different at first, you can still build the same things with them because they have almost all the same pieces.
So, the theorem on formal functions helps us work with these special kinds of numbers so that we can still do math with them even though they don't always behave like regular numbers.
The theorem on formal functions tells us that if we have two formal functions that are equal for all except a finite number of terms, then they are actually the same formal function. This means that we can do operations on these formal functions even if they look a little different from each other.
Think of it like having two sets of legos that look slightly different, but have all the same pieces except for one or two. Even though they may look a little different at first, you can still build the same things with them because they have almost all the same pieces.
So, the theorem on formal functions helps us work with these special kinds of numbers so that we can still do math with them even though they don't always behave like regular numbers.