| Jaydi said: @dsgrue3: I have a good example for you, maybe it will be a good clue to understand why you cannot consider -2 as a solution even if it solves your equation x²=4. |
No, that's meaningless. All I did was abuse substitution as the OP did.
10x = 9.999...
Could lead to 9x = 9 or by substituting on both sides 9*0.999... = 9 (which of course is true only if 0.999... = 1, which is what we're trying to prove. It's circular logic.)
| ebw said: Ironically, a major stumbling block for beginners in computer science is that they have a muddled mental model of variable assignment. When they see an assignment statement like "x=2", a part of them confuses this with the equals sign in math. In mathematical writing, "x=2" is not a variable declaration but merely states that the two sides are equal (one declares a variable by using words like "let", "define", or sparingly, the shorthand ":=" symbol). So the sentence "x=2" holds no more or less information than "2=x". [One exception to this claim: in my own area of math, we often (ab)use the = sign in a way that is not symmetric when describing error estimates. We would write "x = O(n)" to mean that x is bounded by a multiple of n, when formally it would be more appropriate to use element inclusion. Consequently, even if one has "x = O(n)" and "y = O(n)" one cannot deduce that "x=y".] By contrast, in (declarative) programming languages it makes perfect sense to write "x=2" followed later by "x=3", which is mindboggling to a certain number of beginning students. And of course in most languages "2=x" would be an illegal assignment. |
I don't disagree, but I don't see a point here anywhere. Given x = 2 or 2 = x, there is nothing to solve.
| Soleron said: All maths problems effectively start from a "variable declaration". Like, 3x-5=0 is equivalent to a declaration that x=5/3 But if you can't see that straight away you can do a number of steps. But really everything single step is the same as saying "1=1". |
No, they END with a variable declaration. You're solving for x.
You don't start with a declaration and then manipulate it, there isn't a point as it's already known.
