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.
A solution set makes a mathematical sentence TRUE.
Well, honey, a mathematical sentence is like a simple equation or inequality, while a mathematical statement is a broader declaration that can be true or false. So basically, a sentence is just a small piece of the puzzle, while a statement is the whole shebang. Just remember, in math, it's all about precision and not getting your variables in a twist.
a "solution"
True
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.
A solution set makes a mathematical sentence TRUE.
True
True
It depends on the sentence.
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.
Well, honey, a mathematical sentence is like a simple equation or inequality, while a mathematical statement is a broader declaration that can be true or false. So basically, a sentence is just a small piece of the puzzle, while a statement is the whole shebang. Just remember, in math, it's all about precision and not getting your variables in a twist.
A sentence formed using words and mathematical symbols which is either true or false but not both.
identity
Unfortunately the sentence is missing to be able to get the value of x.
That's the "solution" to the equation described by the sentence.
That's the "solution" to the equation described by the sentence.