Limit of distributions

Okay, so imagine you have a big pile of blocks and you want to count how many blocks are in the pile. But instead of simply counting them one by one, you decide to group them into piles of 10. You count how many piles you have and then multiply that number by 10 to get the total count.

Now imagine you have an equation that looks like this: f(x) = 3x+2. However, when you plug in a number for x, such as 1 or 2, you get a different result each time. This is because the equation is a bit "lumpy" and unpredictable. It's like trying to count a pile of blocks that isn't neatly stacked and organized.

This is where the idea of "distributions" comes in. Instead of trying to directly count or evaluate the equation at specific values of x, we can look at how it behaves as x gets bigger and bigger. It's like slowly moving more and more blocks into the pile and watching how the overall shape and size of the pile changes.

The "limit" of a distribution refers to what happens to the overall behavior of the equation as we keep adding blocks, or as x gets closer and closer to some specific value. It's like finding the ultimate size and shape of the block pile after adding an infinite number of blocks.

In the case of the equation f(x) = 3x+2, we can find the limit (or ultimate behavior) as x approaches infinity by noticing that the 3x term will get bigger and bigger while the +2 term becomes relatively insignificant. This means that the overall behavior of the equation will tend towards infinity as well.

Understanding the limit of distributions can help us make sense of tricky equations and better understand the behavior of complex systems in science and math.