Tagged Questions
22
votes
4answers
994 views
Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$?
I can rather easily imagine that some mathematician/logician had the idea to symbolize "it E xists" by $\exists$ - a reversed E - and after that some other (imitative) mathematician/logician had the ...
12
votes
5answers
399 views
Notation Question: What does $\vdash$ mean in logic?
In a "math structures" class at the community college I'm attending (uses the book Discrete Math by Epp, and is basically a discrete math "light" edition), we've been covering some basic logic.
I've ...
10
votes
4answers
2k views
What is the meaning of this symbol ($\models$)?
What's the meaning of this symbol in mathematical notation? :
$\models$
9
votes
2answers
366 views
Formalizing Those Readings of Leibniz Notation that Don't Appeal to Infinitesimals/Differentials
[disclaimer: I've studied a lot of logic but never been good at analysis, so that's the angle I'm coming from below]
in my attempt to find a precise version of the 'definitions' usually given when ...
7
votes
5answers
443 views
'is odd' / 'is even' notation
I would like to write down that $x$ is $true$ if $n$ is odd and $false$ if $n$ is even.
So far I made this up:
$x = ( n - 2⌊\frac{n}{2}⌋ = 1)$
However, I was wondering whether this can be expressed ...
6
votes
3answers
530 views
What's the difference between “$\to$” (implication) and “$\vdash$” (therefore)?
In Wikipedia, here in the last axiom of the Natural deduction system, it says "From [accepting $p$ allows a proof of $q$], infer $(p \to q)$." Isn't that a tautology? In the big table "Basic and ...
6
votes
1answer
243 views
What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
6
votes
3answers
350 views
Difference between $\implies$ and $\;\therefore\;\;$?
I've seen both symbols used to mean "therefore" or logical implication. It seems like $\therefore$ is more frequently used when reaching the conclusion of an argument, while $\implies$ is for ...
5
votes
2answers
121 views
Symbols and terminology for distinguishing derivability from sequents
First some definitions to make it clear what I'm talking about:
A deductive system is a set $J$ of judgments together with a set $R$ of inference rules each of the form
$$ j_0 \leftarrow j_1, ...
4
votes
7answers
281 views
Symbol for “if and only if”: $\implies$ or $\iff$?
I was wondering about the iff sign in maths.
I've never learned about it in school & see it a lot online. Usually the sign looks like this: $\implies$, but in math.stackexchange I always see this: ...
4
votes
6answers
155 views
Negating A Mathematical Statement
Regard this statement $ x \ge 0$. According to my teacher, by negating this statement, it will become $ x < 0$. Why is this so; why does the $\ge$ morph into $<$, and not into $\le$?
4
votes
2answers
357 views
How do you read this logical statement aloud, and how do you notate it in symbols?
Harry Potter and the Methods of Rationality is a wonderful work of fan fiction by AI researcher and decision theorist Eliezer Yudkowsky. In Chapter 39, this exchange takes place between Dumbledore and ...
4
votes
1answer
76 views
“Sum” over logical and?
Given a continuous sequence of integers $(a, a+1, a+2, \dots, b)$ I want to write:
$P_a \wedge P_{a+1} \wedge P_{a+2} \wedge \dots \wedge P_b$
Where $P_i$ is some logical statement parametrized by ...
4
votes
1answer
77 views
Notation in Sacks' 'Higher Recursion Theory'
I'm having trouble with the notation in Sacks' Higher Recursion Theory. I've asked specific questions from page 4. Instead of reading my question in detail and trying to understand my confusion (which ...
4
votes
1answer
165 views
What is the $\tau$ symbol in the Bourbaki text?
I'm reading the first book by Bourbaki (set theory) and he introduces this logical symbol $\tau$ to later define the quantifiers with it. It is such that if $A$ is an assembly possibly contianing $x$ ...
