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All these letters that we use in our calculations are mostly called variables,parameters or name of functions, which are actually variables too. So how do we define variables? For example when we say that x is a real variable what exactly do we mean? Is it a letter that represents any element of the set, so in my example any real number? So if we have defined the set that the variable takes "values" from, then we can apply any operation of this set to specific elements of the set combined with the variable?

To make it more clear, if x is a real variable then we can do all the usual operations to expressions/equations/inequalities etc that contain the letter/variable x? So x is actually a real number and any operation of real numbers can apply to it (example 2*x+3*x=(2+3)*x=5*x=5x) ? This also applies to real functions? I mean f(x) is actually a number ,that can change so it's called a variable, but it's still a real number?

Similar to this, if x is a vector then we can do any operations defined for vectors with x ?

That's all,

Thanks

P.S: Something quite irrelevant: What exactly the equal sign "=" means? When we say that a=b this means that a is exactly the same thing as b?What's the difference with the other sign that i don't know its name, which is similar to "=" but with three lines?

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# Variable definition

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