Constructing Mathematical Statements

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In summary, the speaker has started a new math course and has realized they were never taught how to use symbols to write mathematical statements. They are looking for resources to learn how to construct statements using symbols such as \exists and \forall. They are also unsure if their basic statement, "For all x>4 there exists x>5" \forall x>4 , \exists x>5, is correct and want to learn how to write more complex statements. The suggested resource is the page on first-order logic on Wikipedia, specifically the sections on Provable identities and Provable inference rules. The speaker suggests using these symbols frequently to become more familiar with them, or finding basic analysis books.
  • #1
danago
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Hi. I've just started a new maths course and i have come to realize that i have never been taught how to use symbols to write mathematical statements. For example, up until a day ago, i didnt know what [tex]\exists[/tex] or [tex]\forall[/tex] meant.

Is anybody able to share some links that will explain the use of such symbols to construct statements? I am able to construct really basic statements such as:

"For all x>4 there exists x>5" [tex]\forall x>4 , \exists x>5[/tex]

But i don't even know if what i have written above is correct, or how to write more complex statements.

Thanks in advance,
Dan.
 
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  • #2
you could take a look at

http://en.wikipedia.org/wiki/First-order_logic

maybe it is a bit too general to really helpfull, look especialy at the sections: Provable identities and Provable inference rules, they are very important.

Since you haven't seen these before i guess they are theaching them to you in the class, and the best way to learn it is really just to use them alot. Else try to find some basic analysis books they should teach it. I can't say a specific book because the book i learned it from was in danish so it will probably don't help much.
 
  • #3


Hi Dan,

Thank you for reaching out and seeking resources to better understand mathematical symbols and constructing mathematical statements. It is great that you have identified this gap in your knowledge and are taking steps to fill it.

To start, let's define what mathematical symbols are and why they are important in constructing statements. Mathematical symbols are used to represent mathematical ideas and concepts in a concise and precise manner. They help us express complex ideas and relationships between variables in a compact form. Without symbols, mathematical statements would be lengthy and difficult to understand.

Now, let's address your example statement: "For all x>4 there exists x>5" \forall x>4 , \exists x>5. Your understanding is correct. The symbol \forall means "for all" and \exists means "there exists." The statement can be read as "For all values of x greater than 4, there exists a value of x greater than 5." This statement is true because for any value of x greater than 4, we can always find a value of x that is greater than 5.

To write more complex statements, it is important to understand the logical connectors used in mathematics, such as "and," "or," and "not." These connectors help us combine multiple statements to create more complex ones. For example, "For all x>4, there exists y such that x+y=10" can be written as \forall x>4, \exists y (x+y=10). Here, the logical connector "such that" is represented by the symbol \exists.

To learn more about mathematical symbols and constructing statements, I recommend checking out online resources such as Khan Academy, Math is Fun, and Math Planet. These websites provide explanations, examples, and practice problems to help you better understand and apply mathematical symbols.

I hope this helps. Keep up the good work in your math course and don't hesitate to ask for help when needed. Good luck!
 

1. What is the purpose of constructing mathematical statements?

The purpose of constructing mathematical statements is to express mathematical ideas or relationships in a clear and concise manner. This allows for easier understanding and communication between mathematicians and scientists.

2. How do you construct a mathematical statement?

To construct a mathematical statement, you must first identify the variables and their relationships in the problem. Then, use mathematical symbols and notation to represent these relationships and form a statement that accurately describes the problem.

3. What is the importance of using precise language in mathematical statements?

Precise language is important in mathematical statements because it eliminates ambiguity and ensures that the statement is interpreted in the same way by all individuals. This is crucial in mathematical proofs and calculations where accuracy is essential.

4. Can mathematical statements be proven to be true?

Yes, mathematical statements can be proven to be true using logical reasoning and mathematical principles. This is often done through the use of mathematical proofs, which provide a step-by-step explanation of the reasoning behind a statement.

5. What are some common mistakes to avoid when constructing mathematical statements?

Some common mistakes to avoid when constructing mathematical statements include using vague or imprecise language, making assumptions without proper justification, and using incorrect notation or symbols. It is also important to double check calculations and ensure that the statement accurately reflects the problem at hand.

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