Obviously, there are obvious things in mathematics. Why we should prove them?
- Prove that $\lim\limits_{n\to\infty}\dfrac{1}{n}=0$?
- Prove that $f(x)=x$ is continuous on $\mathbb{R}$?
- $\dotsc$
Just to list few examples.
big-listeducationsoft-question
Obviously, there are obvious things in mathematics. Why we should prove them?
Just to list few examples.
Best Answer
Because sometimes, things that should be "obvious" turn out to be completely false. Here are some examples:
Of course, mathematics has shown that switching doors is to the player's advantage, that Gabriel's horn actually has infinite surface area, that you can indeed get two copies of the original sphere (see Banach-Tarski paradox), and that the Weierstrass function is everywhere continuous but nowhere differentiable. The point being, there are many things out there which are "obvious" but actually turn out to be entirely counterintuitive and opposite what we would otherwise expect. This is the point of rigor: to double check and make sure our intuition is indeed correct, because it isn't always.