by 
Adz3r0
ANSWERS: 4
-
Some mathematical equations cannot be proved for instance 1/0 is undefined. As of this moment no one has been ever able to prove it. + 5
-
Not really. You can write down an equation, say 2x = 10 but this doesn't prove anything. You can use this equation to prove that x=5 but the initial equation itself is not proof of anything.
-
Not at all! I would argue that some are not proven but explain something, like a linear equation showing a relationship from statistical analysis. However, you can 'prove' that the derivative is equal to the tangent of the line and is thus the slope.
-
A proof is a sequence of true statements each of which follow from previous statements, or from "axioms", following rules of inference. An axiom is a statement taken to be true to start things off. Now in one system of math, a = a is an axiom, saying that the symbol 'a' is equal to the symbol 'a'. In this system there is a rule that says you can substitute anything for a, as long as you do it once only for each and every 'a' in the original. Therefore, 1 = 1 is a true equation which forms the last and only line of its own proof. But not all equations are proofs by themselves, or even true. P.S. It sounds like everything rests on these rickety axioms - how do we know they are true? But this is just one way of looking at it. The very early axioms exist even before meaning has been given to the early symbols. In "a = a", what exactly does '=' mean? The axioms basically set down rules for how the symbols like '=' behave.
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC