MHB How do I understand notational mathematics?

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The discussion centers on the challenge of understanding and writing the formula for the Cartesian product in the context of theoretical computer science mathematics. The participant expresses frustration with grasping the formal definitions, despite having a solid understanding of the concepts and having excelled in discrete mathematics. The conversation highlights the importance of definitions in mathematics, as they form the foundation for theorems and proofs. Recommendations include reviewing chapters on set theory and logic in discrete mathematics textbooks, which typically cover the necessary notations and definitions. The emphasis is on overcoming barriers to understanding formal mathematical language to facilitate further learning in the field.
shivajikobardan
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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.
1649844774394.png

Similarly, in other cases
1649844857518.png

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 theoritical computer science mathematics.
I want to get above this barrier. Any guidance you can recommend?
 
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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.
 
Evgeny.Makarov said:
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.
 
shivajikobardan said:
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.
 
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