Τ-additivity

Okay kiddo, today we are going to learn about something called τ-additivity. It might sound like a big word, but it's actually pretty simple.

Let's first talk about what 'τ' means. It's a symbol that stands for a set of numbers. So, if I say τ = {1, 2, 3}, it means that the set τ contains the numbers 1, 2, and 3.

Now, let's move onto 'additivity'. This means that we are adding things together. For example, if I have 2 apples and you give me 3 more apples, then we add them together to get 5 apples.

So, when we talk about τ-additivity, we are essentially adding up sets of numbers that are represented by the symbol τ.

But here's the tricky part - in τ-additivity, we only add up the sets if they don't overlap. What does that mean? It means that if two sets share some of the same numbers, we can't just add them together like we did with the apples. Instead, we have to subtract the overlapping numbers first, and then add the remaining numbers together.

Let me give you an example. Let's say we have two sets: τ1 = {1, 2, 3} and τ2 = {2, 3, 4}. They have numbers 2 and 3 in common, which means there's an overlap. So, to add them together using τ-additivity, we have to subtract the overlap first. That means we take away the numbers 2 and 3 from one of the sets (let's say τ2), and then we add the remaining numbers together like this:

τ1 + τ2 = {1, 2, 3} + {4}
= {1, 2, 3, 4}

So, in conclusion, τ-additivity is a way of adding up sets of numbers represented by the symbol τ, but only if they don't overlap. If there's an overlap, we have to subtract the overlapping numbers first before adding them together.