Intereting Posts

What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
what is the proof for $\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)} = \frac{1}{4} $
Isn't $x^2+1 $ irreducible in $\mathbb Z$, then why is $\langle x^2+1 \rangle$ not a maximal ideal in $\mathbb Z?$
Prove that the Completeness Axiom follows from the Least Upper Bound Principle.
Some iterate of a linear operator over $\mathbf F_q$ is a projection
Prove $f(x)=\int\frac{e^x}{x}\mathrm dx$ is not an elementary function
$e$ to 50 billion decimal places
Proving the Kronecker Weber Theorem for Quadratic Extensions
Is the square root of a negative number defined?
What's the name of the approximation $(1+x)^n \approx 1 + xn$?
If $S \times \Bbb{R}^k$ is homeomorphic to $T \times \Bbb{R}^k$ and $S$ is compact, can we conclude that $T$ is compact?
$K_n$ as an union of bipartite graphs
Kähler differential over a field
Prove the set of which sin(nx) converges has Lebesgue measure zero (from Baby Rudin Chapter 11)
A common term for $a_n=\begin{cases} 2a_{n-1} & \text{if } n\ \text{ is even, }\\ 2a_{n-1}+1 & \text{if } n\ \text{ is odd. } \end{cases}$

The symbols $\forall$ and $\exists$ denote “for all” and “there exists” quantifiers. In some papers, I saw the (not so common) quantifiers $Я$ and $\exists^+$, denoting “for a randomly chosen element of” and “for most elements in”, respectively.

Are there other symbols for quantifiers?

I’m specially interested in quantifiers for:

- Notation for “vectorized” function
- Etymology of $\arccos$, $\arcsin$ & $\arctan$?
- e-notation scientific notation
- What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
- Why are x and y such common variables in today's equations? How did their use originate?
- What means a “$\setminus$” logic symbol?

- for all but finitely many elements of…
- for infinitely many elements of…

**Edit:** After seeing some of the comments, I found the list of logic symbols and the table of mathematical symbols, which I could be useful for others.

- Why when dividing by $ 2 \pi$ does something increase
- The notations change as we grow up
- What is the “status” of the rule that multiplication precedes addition.
- Example of a very simple math statement in old literature which is (verbatim) a pain to understand
- In generatingfunctionology, for a polynomial $P$ and a differential operator $D$, what does $P(xD)$ mean?
- Qualification of a Universal Quantification
- Big Greeks and commutation
- Difference Between “$\forall x \exists y$” and “$\exists y \forall x$”
- Frequency of Math Symbols
- Why does $\bigcap_{m = 1}^\infty ( \bigcup_{n = m}^\infty A_n)$ mean limsup of sequence of set?

The most commonly used symbols to express “for all but finitely many” and “there are infinitely many” are $\forall^\infty$ and $\exists^\infty$, respectively.

Not quite a symbol per se, but of course there is “a.e.” (“almost everywhere”): “for all but a set of measure zero”. Probabilists call it “a.s.” (“almost surely”). They are also in the habit of writing “a.a.” (“almost all”): “for all but finitely many” and “i.o.” (“infinitely often”): “for infinitely many”.

In potential theory, one also sees “q.e.” (“quasi-everywhere”): “for all but a set of capacity zero”.

Have seen a symbol that looks somewhat like $\forall \!\!\!\! – $ or $ \large \vee \!\!\!\!\!\!\! = $ frequently used by my teachers for “for all but finitely many” (equivalently, “for all large enough” in the context of natural numbers). Ergo, used that frequently myself in class. Surprised to find that it is not as standard as I have always taken it to be.

Jaśkowski used $\Pi$ for quantifying over propositions. So he would write

$$\Pi a . \Pi b. a \to b \to a$$

It is useful for formalizing things like “does double negation elimination imply LEM”, which you have to write as

$$(\Pi a. \lnot \lnot a \to a) \to (b \lor \lnot b)$$

IIRC he used $\Sigma$ for existential quantification over propositions.

- Prove that $(ma, mb) = |m|(a, b)$
- Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
- How to study math from arithmetic level?
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- The maximum product of two numbers which together contain all non-zero digits exactly once
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- $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer.
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- What is the color number of the 3D space, if we allow only convex regions?
- Probability of a substring occurring in a string
- Ramanujan's First Letter to Hardy and the Number of $3$-Smooth Integers
- What does “removing a point” have to do with homeomorphisms?
- What is the Euclidean function for $\mathbb{Z}$?
- Proof of L'Hopital's rule
- How to evaluate $\int_{0}^{1}{\frac{{{\ln }^{2}}\left( 1-x \right){{\ln }^{2}}\left( 1+x \right)}{1+x}dx}$