How do I understand notational mathematics?

[shivajikobardan]

I will try to explain what I mean.
I understand how to calculate cartesian product. but I can't write the formula for cartesian product as shown below.

Similarly, in other cases

I understand what it is trying to say(the inituition) but I really don't understand a word written in it. I feel like this is a huge road block in my journey of learning theoretical computer science mathematics.
I want to get above this barrier. Any guidance you can recommend?

 

[Evgeny.Makarov]

Perhaps you need to read chapters on set theory and logic in any discrete mathematics textbook.

The Cartesian product formula uses the set-builder notation.

 

[shivajikobardan]

Perhaps you need to read chapters on set theory and logic in any discrete mathematics textbook.

The Cartesian product formula uses the set-builder notation.

I already studied discrete math and passed with flying colors. We didn't have to write definitions It was based on understanding. I understand how to solve them, the gist, the inituition but can't understand and memorize these definitions.

 

[Evgeny.Makarov]

We didn't have to write definitions It was based on understanding.

Mathematics starts with definitions, which are followed by theorem statements and their proofs. Without definitions there are no objects to talk about.

In any case, every discrete mathematics textbook has a discussion of notations used in the two pictures you posted. If you have specific questions, you are welcome to ask them here as well.