Is this you? As a journalist, you can create a free Muck Rack account to customize your profile, list your contact preferences, and upload a portfolio of your best work.
Claim your profile
Yes, $\mathbb N=\{1,2,3\ldots\}$ and is also different from the set of positive integers. The reason is because the elements $1,2,3,\ldots$ are not the same $1,2,3,\ldots$ in the set of positive integers. They only appear to be. Starting from the ZFC axioms it is easy to deduce that there is a set of natural numbers $\mathbb N$ on which a binary operation $+$ can be defined. We can also define multiplication, and order on this set.
Probably the formula is the way it is for historical reasons. Generally speaking, our intuition of "steepness" matches the definition of slope: the steeper a line is, the higher is its slope in absolute value. This works with slope equal to $\text{rise} / \text{run}$, but would not work if the slope were equal to $\text{run} / \text{rise}$ as you suggest. For a modern example, when you drive down a steep mountain highway, you will notice signs saying something like "Danger: 5% grade ahead.
As a journalist, you can create a free Muck Rack account to customize your profile, list your contact preferences, and upload a portfolio of your best work.
