Unbounded operator

Okay kiddo, an unbounded operator is like a big math rule that you can use to change one thing into another thing. But sometimes, that math rule doesn't work for every possible thing you could give it.

It's kind of like a toy car track that comes in pieces. You can connect the pieces in different ways to make different tracks. But if you want to make a really long track, you might need more pieces than you have, so the track can't go on forever.

The same thing happens with unbounded operators. They can't always work for every number or thing you could give them. Sometimes, they only work for a few things or a certain range of things. So we say that these operators are "unbounded" because they don't work for everything.

But don't worry too much about that, kiddo. Just think of unbounded operators as math rules that work really well for most things, but not always for everything.