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The word for a statement that is true for any number or variable is a "universal statement" or a "universal quantification." In mathematical logic, this type of statement is typically denoted using the universal quantifier symbol (∀), which signifies "for all" or "for every." Universal statements are used to make generalizations that apply to all elements in a given set or domain.
An identity.
It is called an identity.
no
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An identity.
It is called an identity.
no
It is triple the number of edges on one base.
linear equation in one variable
Yes, IF the variable has been declared, has a value, and is of a numerical type such that your addition operator can perform the operation on the number and the value of that type variable. The compiler or interpreter will look up the variable's value, substitute it for the variable, and perform the addition just as if your statement used two numbers. First example: If your number is an integer and your variable is of type real, almost any addition operator can successfully add the two. Second example: If your number is a real and your variable is a character type (with a value, say, of "Smith"), the addition will obviously fail. In many languages, however, variables of type Boolean may be handled arithmetically, as the value True equals 1 and False is zero.
Yes, that term is used in math. Consider an equation; I'll use a simple one: 2x = 14 This is a statement about the equality of the two sides; it is stated that 2, multiplied by "x", is equal to 14. Depending on the value of "x", this statement can be true, or false. In this case, if you replace "x" with 7, the statement is true; if you replace it by any other value, it is NOT true. The equation is said to be "satisfied" by any value which, when replaced for the variable, converts it into a true statement - in this case, 7.
No. In COBOL, any variable must be declared with PIC statement.
In algebra, variables are represented by letters such as x. A variable could be any number. That number is the "value" of the variable. In an expression, you can choose a number to put in for x, and simplify to get a number which is the value of the expression. In an equation, you can solve for the value of x, which will be the value of x which makes the equation true.
A linear equation in one variable. Case 1: A conditional equation: True only for a value of the variable. Ex. x + 2 = 3, True only when x is 1. Case 2: Identity Equation: Always true. Ex. x + 2 = x + 2, True for any value of x. Case 3: x + 1 = x + 5, False for any value of x. We call a solution any value of the variable that satisfies the equation, meaning if we replace the variable with that value, the equation becomes a true statement. Example: -2(x -3) = 8 - 2x -2x + 6 = 8 - 2x (add 2x and subtract 6 to both sides) 0 = 2 False. Since this equation, which is equivalent to the original equation, is false, then the original equation is also false. Meaning, there is no real number for x that could satisfy the equation. So there is no solution to the equation.
A statement in maths is true only if it is proved by a series of mathematical manipulations and logic for any GENERAL number for which the statement should satisfy. Otherwise, it is only a conjecture. This is the beauty of mathematics and it is proof which differentiate mathematics from all other fields.