 Let's have one more complex topic, is this notion of a limit of infinity. When talking about these limits, it's helpful to describe quantities using two sets of adjectives that denote either the sine, we say that something is positive or negative, and of course we use the symbols plus or minus, and magnitude, something is either large or small, and we'll use the symbols infinity or zero for these things. And so if we want to talk about something that is a large positive number, we might write plus infinity, and if we want to talk about something that is a small negative number, we might write zero, indicating small, and superscripting a minus to indicate negative. And the following ideas are helpful to remember when you divide, a number divided by a large number is a small number, meanwhile a number divided by a small number is a large number. So let's take a look at the limit as x approaches 5 from above of 1 over 5 minus x, the limit at fx approaches 5 from below, and the limit as x approaches 5. So at x equals 5, 1 over 5 minus x is undefined, but who cares, the value of f of x at x equals a is not relevant to the limit as x approaches a. So if I want to find the limit as x gets close to 5 from above, so x is a little bit more than 5, then 5 minus x is small negative, and so I might indicate that as a zero with the superscripted minus, and that means 1 over 5 minus x is going to go to 1 over small negative number. And when I divide 1 by a small negative number, I get a large negative number, and so I can write that as minus infinity, and so our limit is going to be minus infinity. Similarly, as x approaches 5 from below, a little bit less than 5, then 5 minus x is going to get close to a small positive number. So 1 over 5 minus x is 1 over a small positive number, which will be a large positive number, and so our limit as x approaches 5 from below is going to be infinity. And finally, since the limits do not agree, the limit as x approaches 5 of 1 over 5 minus x is non-existent.