What are p-adic numbers?

P-adic numbers are like having a special way to measure how close numbers are, but not like regular distances, it's more like counting how many times you can divide one number by another.

Imagine you're playing with blocks. If you have 100 blocks and you want to see how similar it is to 99 blocks, normally you'd say they’re just 1 block apart. But with p-adic numbers, especially 2-adic numbers, if we're using 2 as our special number, we look at how many times each number can be divided by 2.

So, 100 is like 2 × 2 × 5 × 5, and 99 is just a bunch of odd numbers. That means 100 is "closer" to 0 in the 2-adic world because it has more factors of 2.

Think of p-adic numbers like a game where you get points for how many times your number can be divided by p, which could be any number, like 3 or 5. The more divisions you have, the "closer" your number is to zero in that world.

It's kind of like having different rulers, one measures length, and another counts how many times something fits into it. P-adic numbers give us a whole new way to see numbers! P-adic numbers are like having a special way to measure how close numbers are, but not like regular distances, it's more like counting how many times you can divide one number by another.

Imagine you're playing with blocks. If you have 100 blocks and you want to see how similar it is to 99 blocks, normally you'd say they’re just 1 block apart. But with p-adic numbers, especially 2-adic numbers, if we're using 2 as our special number, we look at how many times each number can be divided by 2.

So, 100 is like 2 × 2 × 5 × 5, and 99 is just a bunch of odd numbers. That means 100 is "closer" to 0 in the 2-adic world because it has more factors of 2.