Counting is a very fundamental skills that I think can be overlooked when you're first introduced to math. Most importantly, the difference between counting a distances and elements.

Lets look at two ways of counting based on the follow set of numbers.

$${1,2,3,4,5,6}$$

Counting Distances

• The distance is the amount of increments or decrements until you reach your target.
• You can represent the distance as a sequence of jumps to the target.

For instance, the distance between 1 and 4 is 3 because by incrementation 2, 3, 4 are the values jumped to before reaching 4.

• An easy way to calculate distances is by simply calculating the difference between the destination and start: $$4-1=3$$

Counting Elements

To count elements we look at the interval instead of the distance. How many elements are in the closed interval $[2,5]$? you might say well it's the distance between $5$ and $2$ or $5-2$ which is $3$, but this is wrong because the distance formula doesn't take into account the initial value, which is included in the interval.

• To calculate the number of elements you must include an extra to account for the start: $$5-2+1=4$$