There is a specific name for the symbol that’s used in mathematics to denote “approximately equal” — and it’s one of the most commonly used symbols in mathematical notation.
It might not seem like much, but the approximate symbol has played a central role in how we do math. And it plays an even more important role when we move into applied fields such as engineering or physics, where exact measurements are sometimes unattainable and precise calculations are unnecessary. (And don’t think you can skip over this symbol if you’re working with computers, either!)
What’s the difference between = and ≠? Well, the equals sign denotes that two quantities are exactly equal; the inequality sign means they are unequal. But what about the approximation sign?
The ≈ symbol is known formally as the approximately equal sign. That is, any values placed before and after the ≈ symbol should be considered “nearly equal,” although there will likely be some small discrepancy between them. In many cases, those values are close enough to be used interchangeably within the context of the discussion at hand.
In numerical terms, this often refers to the situation in which the result of an operation cannot be expressed as an exact number. Instead, we have to accept that it’s either an infinite decimal expansion (such as 1/3) or an irrational quantity, such as pi, which goes on infinitely without repeating itself.
When we use the approximation symbol, then, we’re indicating that a value is close enough to what we want for our purposes, whether it be the topic of our analysis or the outcome of our calculation.
This concept of “approximate equality” is especially crucial in fields like engineering, physics and computer science, where precise measurement is essential, yet perfect accuracy is often neither possible nor necessary. Understanding how the approximation symbol functions in relation to the equals sign is part of mastering mathematical notation.
A Related Symbol With a Different Meaning
A similar symbol appears in Unicode under the name “approximately equal to” (U+2252). This symbol can mean two things depending on the context: it may indicate “approximately equal to” or the image of. This can cause confusion, so the context is important.
For example, in experimental physics, the gravitational constant G is approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2. We know that this value isn’t quite accurate enough, but it’s good enough for our purposes. On the other hand, in set theory and mappings, the symbol could mean something completely different.
Let’s say f maps from X to Y, where y is an element of Y, and x is an element of X. If y is the image of x, then we would write x ≒ y. In this case, the meaning is different than if you see it used elsewhere.
So, again, context is key to understanding what these two symbols mean.