Degeneracy (mathematics)

Have you ever played with Legos or blocks? Imagine you have a set of colored blocks and you want to make a tower. You can make a tall tower by stacking the blocks one on top of the other in a straight line. This is called a "regular" tower because there is only one way to make it.

But what if you have blocks that are the same color and size, and you want to make a tower but it doesn't have to be straight? You can try stacking them in different ways, like making a zigzag or a pyramid. This is called a "degenerate" tower because there are many ways to make it and still end up with the same height.

In math, degeneracy means there are different ways to get the same result. For example, if you have an equation like 2x + 4y = 8, there are many different values of x and y that will make the equation true. These values are called "solutions." In this case, (2,1), (0,2), and (4,0) are all solutions because when you plug them into the equation, you get 8.

So, degeneracy in math means that there are multiple ways to achieve the same outcome or solution. It is important to understand degeneracy because it can help us find more than one solution to a problem and give us more flexibility in our thinking.