Ordered exponential field

A field is like a playground where numbers can play. An ordered field is a playground where the numbers can be put in order, like lining up for lunch. An exponential field is a playground where you can use powers, like multiplying a number by itself multiple times.

An ordered exponential field is a playground where the numbers can be put in order, you can use powers and it has a special rule that says you can't have a number that is between 0 and 1 that you can't get by taking a power of another number between 0 and 1. It's like making sure all the kids are in order from smallest to biggest and making sure that every kid in line has a buddy from the line behind them.

So, basically, an ordered exponential field is a special playground where you can do different math things and make sure everyone has a buddy!