I don’t know whether the following pattern was intentional, but it’s at least a mnemonic. (These are also called surjective functions or epimorphisms.) This is U+21A0 or \twoheadrightarrow in LaTeX. Onto functions are denoted with an arrow with two heads. (These are also called injective functions or monomorphisms.) This is U+21A3 or \rightarrowtail in LaTeX. One-to-one functions are denoted with an arrow with a split tail. These decorations aren’t entirely standard, so it’s hard (at least for me) to remember what they mean. Mathematicians sometimes decorate arrows in diagrams to encode more information about what the arrow represents. I’m betting that more people will be able to see glyphs for the Latin letters than for the correct symbols. That’s because font support for Unicode is poor. If you look at the source for this page, you’ll see that I deliberately use the wrong characters for h and ħ. LaTeX does not have a special command for h because it does not make semantic distinctions between visually identical characters.
If you’re wondering why anyone should care about making such distinctions, see this post.
Meanings of calculus symbols code#
Also, there is a character ħ in the Latin Extended-A portion of Unicode, U+0127 (LATIN SMALL LETTER H WITH STROKE), but the correct code point for ħ is U+210F (PLANCK CONSTANT OVER TWO PI).
The correct Unicode value for h is U+210E (PLANCK CONSTANT), not simply the common h U+0068 (LATIN SMALL LETTER H). The symbol ħ is simply pronounced “h bar” and is sometimes called the reduced Planck constant. When working with angular frequency ω = 2πν, it is convenient to introduce a new constant ħ equal to h/2π so that E = ħω. In physics, Planck’s constant is the proportionality constant between energy and particle frequency: E = hν. I think the original understanding of the phrase was that if exceptions are remarkable, that shows that the rule often holds.
Wikipedia says “Ш has the distinction of being the only distinctly Cyrillic letter internationally used in mathematics.” Also according to Wikipedia, sha probably comes form the modern Hebrew Shin letter (ש, U+05E9).īy the way, the phrase “the exception that proves the rule” doesn’t make sense as commonly interpreted. Sha is apparently an exception that proves the rule that Cyrillic letters are seldom used in math (at least in the West). I’d seen the Dirac comb before, but I don’t recall Ш being used as a symbol for it. The letter sha is also used in distribution theory for the “Dirac comb,” an infinite sum of evenly spaced delta functions. It is used for the Tate–Shafarevich group of an Abelian variety. Andres Caicedo pointed out that the Cyrillic letter sha (Ш, U+0428) is an exception. I mentioned in a conversation that math rarely uses Hebrew or Russian letters. The symbols ⊤ (U+22A4) and ⊥ (U+22A5) \top and \bot in LaTeX. The symbols ⊢ (U+22A2) and ⊣ (U+22A3) are \vdash and \dashv in LaTeX. x ⊣⊢ y means x and y are each provable from the other. Both expressions together are used for equivalence, i.e. Likewise x ⊣ y means that x is provable from y. The expression x ⊢ y means that y is provable from x. Logic also uses symbols that look like a T rotated 90 ° clockwise or counterclockwise, ⊢ (U+22A2) and ⊣ (U+22A3). Logic uses a symbol that looks like a sans serif T (⊤, U+22A4) to denote “true.” The same symbol turned upside down (⊥, U+22A5) is used for “false.” An advantage of using this symbol rather than some form of F is that it makes the symmetry of some formulas more apparent. The mathematical significance of the Weierstrass ℘ function is that all elliptic functions can be expressed as rational functions of this function and its derivatives. The symbol is described in Unicode as U+2118 (SCRIPT CAPITAL P). Mathematicians don’t often change the style of letters to denote special functions, but the Weierstrass ℘ function is a notable exception. The non-mathematical posts are collected here. This page contains the math-related posts from my short-lived blog Symbolism.
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