One-parameter semigroup

A one-parameter semigroup is like a group but with only one parameter. Imagine you have a toy car and you can control how fast it drives. The car moves forward or backward depending on how fast you make it go. That's like the one parameter for the one-parameter semigroup.

Now, let's think of a dough rising in the oven. It's like the car moving forward because it gets bigger and bigger over time. If we turn off the oven, the dough shrink but never disappears. That's also like the semigroup. It changes over time but it doesn't go away completely.

So, to understand the one-parameter semigroup, just think of it like a toy car you can control the speed of or dough rising in the oven that changes over time. It's like a group but only with one parameter to control it.