Extension by definitions

Imagine you have a pretend cookie jar. Sometimes, someone might tell you that you can only put certain things in the jar, like cookies or crackers. This is like a definition of what can go in the jar.

Now, let's say you learn a new word - "treats". You're not quite sure if treats can go in the cookie jar because you're not sure if treats count as cookies or crackers. So, you ask the person who made the original rule if treats are allowed.

They might say "Yes! Treats are allowed in the cookie jar!" This is called an extension of the original rule by definition. It means that the original rule has been expanded to include a new type of thing that fits the definition.

In the same way, in language and logic, when a new symbol is introduced, its meaning can be extended by definition to include new situations. This makes it easier to use and understand the symbol in a wider variety of contexts.