Squeeze theorem
The Squeeze Theorem is like a game of "King of the Hill". In this game, three mountains are drawn side by side. The highest point of each mountain is marked with a flag. To win the game, your goal is to get your flag to the top of the middle mountain.
You start by putting your flag on the lowest point on the left mountain. You then start to move your flag up the mountain, a little bit at a time. Every time you move your flag up the mountain, you can look to the right and see how close you are getting to the top of the middle mountain.
Eventually, you will come to two points between the two mountains where you can't move up anymore. These points are called the left and right bounds of the middle mountain. No matter what you do, you can never get past either of these points.
Even though you can't move up the mountain anymore, you still haven't made it to the top. This is where the Squeeze Theorem comes in. The Squeeze Theorem says that if you keep squeezing the two mountains closer together (without actually letting either of them move), then eventually your flag will reach the top of the middle mountain. No matter what happens, you will eventually get to the top.
You start by putting your flag on the lowest point on the left mountain. You then start to move your flag up the mountain, a little bit at a time. Every time you move your flag up the mountain, you can look to the right and see how close you are getting to the top of the middle mountain.
Eventually, you will come to two points between the two mountains where you can't move up anymore. These points are called the left and right bounds of the middle mountain. No matter what you do, you can never get past either of these points.
Even though you can't move up the mountain anymore, you still haven't made it to the top. This is where the Squeeze Theorem comes in. The Squeeze Theorem says that if you keep squeezing the two mountains closer together (without actually letting either of them move), then eventually your flag will reach the top of the middle mountain. No matter what happens, you will eventually get to the top.