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What do you mean by a "mathematical sentence"?

In some practice in analysis (Calculus stuff), we call a statement a sentence if it looks like one or any combination of the following:

"For all a in set A, condition P(a) is true/false"

"There exist some (or unique) a in set A where P(a) is true/false"

So in that practice, your statement is NOT a sentence, but if you phrase it

"There exist a unique x in our set where x = 0 is true" or simply

"There exist a unique element x where x = 0" It would be a sentence.

BUT, I am pretty sure what I am talking about is not the same "mathematical sentence" as yours.

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Q: Is x equals 0 a mathematical sentence?
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If 0X0 equals 00 plus 0 equals 0 and 2X2 equals 42 plus 2 equals 4 so what is another number which after multiply and addition answer the same way?

0 and 2 are the only such numbers. Here's the mathematical proof.Stated mathematically, the question is, for what number xis it true that x plus x is equal to x times x:x + x = x * xThis reduces to:2x = x2We can then rearrange this as a simple quadratic equation:x2 - 2x = 0This can be factored to:x (x - 2) = 0Which has the two real solutions x = 0 and x = 2.


What is the definition of a mathematical sentence?

Basically, a sentence is a formula which is either true or false, e.g. 1 < 2 (it is true of course), 0 = 1 (this is false, but still a sentence). [We'll assume we are working with real numbers....] If you have variables, they must be "quantified", that is, you either say that the formula holds for every value of the variable, or for some (possibly unknown) value of the variable. 1) 1+2 = 3 2) x+2 = 3 3) x+2 = 3, for some x 4) x+2 = 3, for every x 1 is a true sentence, 2 is not a sentence, 3 is a true sentence (since x=1 is a solution), 4 is a false sentence (because x=0 is an example for which the formula is false). A mathematical sentence in algebra is also known as an expression. An expression can be defined as a sentence that has a number, an operation, and a letter in it. When a mathematical sentence is not in algebraic form, it just has to have two numbers and an operation.


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Is xy equals 0 - x equals 0 or y equals 0 a biconditional statement?

maybe