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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.
A solution set is all the numbers that make a mathematical sentence is called a what?
A solution set makes a mathematical sentence TRUE.
Replace a variable with a value that results in a true sentence is what?
Oh, what a happy little question you have there! When we replace a variable with a value in an equation or sentence and it makes the sentence true, we're finding a solution that works perfectly. It's like adding a touch of color to a blank canvas, bringing harmony and balance to the mathematical world. Just remember, there are infinite possibilities waiting to be discovered!
What is the difference between a mathematical sentence and a mathematical statement?
A mathematical sentence is a specific type of mathematical statement that uses mathematical symbols and operations to express a relationship or equation, such as 2 + 3 = 5. A mathematical statement, on the other hand, is a broader term that encompasses any declarative sentence in mathematics, including theorems, definitions, and conjectures. In summary, all mathematical sentences are mathematical statements, but not all mathematical statements are necessarily mathematical sentences.
The value for a variable that results in a true sentence is called an?
a "solution"
