## This article created 13 December 2019 by Deven Blake

Interval notation is a way to express intervals in terms of numbers.[1]

Take, for example, the inequality x < 5, where x can be any number lower than five. This inequality also represents an interval; x exists within the interval between the lowest number possible and five, excluding negative-infinity (because that unfortunately is not a number) and excluding five (because x has to be *less than* five). Mathemeticians try to express things like intervals with symbols rather than language, because not all mathematicians speak English (and I can tell you from personal experience that many of my peers exclusively speak English) - we do that by putting intervals in this interval notation.

So, in `x < 5`, the lower exclusive bound is -infinity, and the upper exclusive bound is five. Interval notation dictates exclusive bounds to be marked with parentheses- keep in mind that these parentheses are not grouping symbols, so be careful to not read interval notation like you would a math equation. The bounds face into the equation, so this `x < 5` becomes (-∞, five) - with a comma to separate the bounds.

But what if we had `x <= 5`? How do we differentiate the now inclusive boundary at five from the exclusive boundary? In interval notation brackets are used rather than parentheses for inclusive boundaries, but *only* for inclusive boundaries. A right bracket may not have a left bracket, or vice versa! This is something worth taking note of; if you're used to writing mathematical equations you may get the itch to pair that parenthesis with another parenthesis. Don't. In sum, this `x <= 5` becomes `(-∞, 5]`, because the lower bound (exclusive) is at negative infinity and the upper bound (inclusive this time) is five.

[1]: Mathwords - Interval Notation