¹ I went to school and studied physics and math in Germany. Works of the same author using ~ only when technical restrictions applied.Examples of ~ being used for this purpose in systems that do not technically favour this symbol.Is there any harder evidence that the usage of ~ for “approximately equal” is a consequence of it being a makeshift solution in light of technical restrictions? I do not want to debate what is right™ here, but I am just curious whether this usage is a result of the limitations of typewriters and predominant keyboard layouts and encodings from the early days of computing, which make ≈ difficult to produce or impossible to encode, while ~ is readily available.īy contrast, I would expect that in moveable type (and similar systems that do not allow superimposing characters), you either had both or neither glyphs available, as I am not aware of any relevant application for the ~ glyph besides equations in such systems².Īlso, in TeX, both symbols are comparably difficult to use ( \approx and \sim). Yet, I often see the symbol ~ used for “approximately equal” in the scientific literature, in particular in fields where TeX use is scarce. The symbol ~ was only used for more mathematical purposes such as equivalence, proportionality, or “is distributed as”.
These symbols more commonly have one end closed with the other end open, suggesting which side is "bigger.In my life¹, I have never seen a symbol other than ≈ used in handwriting to express “approximately equal”. Similarly to how there are many symbols for equivalence relations ( or equivalence-like relations) in use, there are many different symbols for orders and partial orders, such as $<,\leq,\prec,\preceq,\subset,\subseteq\dots$, again with some orders exclusively using one symbol over another but symbols being used for multiple things. ( Note that this example is not an equivalence relation since the relation is not transitive., $9.82\not\approx 10.47$).Īs for what the symbols are named, I am in the habit of either referring to them by the name of the relation they are being used to represent, or referring to them by their $\LaTeX$ designation ($\simeq$ being called "simeq" for example)
Here we would have something like $10.47\approx 10$ and also $9.82\approx 10$.
For example $\approx$ might represent the relation " is close in value to" where we say for example $a\approx b$ iff $|a-b|<0.5$. There are some situations where those symbols which have squiggles may be used to represent relations which are not true equivalence relations, but act similarly to equivalence relations. On the other hand, most if not all symbols in that list can be used for multiple different situations, such as how we use $=$ to represent equality between real numbers, equality between matrices, equality between sets, etc. On the other hand, some equivalence relations do not have a universally designated symbol to use, so any from that list ( or similar to those in that list) may be used and is largely author preference. Some specific equivalence relations may have standard choices for which symbol to use ( such as how our usual equality is almost always represented by $=$). Symbols such as $\sim,\approx,\simeq,\approxeq,=,\equiv,\fallingdotseq,\risingdotseq,\doteqdot,\dots$ where lines are generally parallel or squiggles generally represent equivalence relations.
0 kommentar(er)
