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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The functions g and f are said to commute with each other if g ∘ f = f ∘ g. Commutativity is a special property, attained only by particular functions, and often in special circumstances. For example, | x | + 3 = | x + 3 | only when x ≥ 0. The picture shows another example. The composition of one-to-one (injective) functions is always one ...
Given the function symbols F and G, one can introduce a new function symbol F ∘ G, the composition of F and G, satisfying (F ∘ G)(X) = F(G(X)), for all X. Of course, the right side of this equation doesn't make sense in typed logic unless the domain type of F matches the codomain type of G, so this is required for the composition to be defined.
A function symbol, with some valence greater than or equal to 0. These are often denoted by lowercase roman letters such as f, g and h. Examples: f(x) may be interpreted as "the father of x". In arithmetic, it may stand for "-x". In set theory, it may stand for "the power set of x". In arithmetic, g(x,y) may stand for "x+y".
Open E with dot below: George Herzog’s Jabo transcription Ɛ̣̀ ɛ̣̀: Open E with dot below and grave: Ɛ̣́ ɛ̣́: Open E with dot below and acute: Ɛ̣̂ ɛ̣̂: Open E with dot below and circumflex: Ɛ̣̃ ɛ̣̃: Open E with dot below and tilde: Ɛ̣̈ ɛ̣̈: Open E with dot below and diaeresis: Ɛ̣̈̀ ɛ̣̈̀: Open E with dot ...
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
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The Phonetic Extensions block has several superscripted letters and symbols: Latin/IPA ᴬ ᴭ ᴮ ᴯ ᴰ ᴱ ᴲ ᴳ ᴴ ᴵ ᴶ ᴷ ᴸ ᴹ ᴺ ᴻ ᴼ ᴽ ᴾ ᴿ ᵀ ᵁ ᵂ ᵃ ᵄ ᵅ ᵆ ᵇ ᵈ ᵉ ᵊ ᵋ ᵌ ᵍ ᵏ ᵐ ᵑ ᵒ ᵓ ᵖ ᵗ ᵘ ᵚ ᵛ, Greek ᵝ ᵞ ᵟ ᵠ ᵡ, Cyrillic ᵸ, other ᵎ ᵔ ᵕ ᵙ ᵜ.