Linked Questions

1
vote
0answers
36 views

notation in definition of range and domain [duplicate]

In my set theory book (A book of set theory, Charles,C,Pinter) domain and range of graph $G$ is defined by $dom G=\{x:\exists y \ni (x,y)\in G\}$ $ran G=\{y:\exists x \ni (x,y)\in G\}$ But I don't ...
24
votes
6answers
85k views

Symbol for “such that” (not in set)

If $A$ is a set, we can use the set notation $$A= \{ b \mid\text{property $p_1$ of $b$}\}$$ But say $A$ is an element like $b$, $$A = b \mid \text{property $p_1$ of $b$}$$ is this a usual ...
13
votes
4answers
961 views

Do people whose native languages are read right-to-left experience mathematical statements differently? [closed]

When I see the equation $$A = B$$ the first idea to occur to me is that $A$ can be transformed into $B$. Although of course $$B = A$$ has the same content, to me it connotes rather that $B$ can be ...
5
votes
2answers
28k views

What does the symbol described below mean? (looks like: sideway u with a line through the middle)

The symbol kind of looks like this: ε, but it's more like a sideways u with a line through the middle.
2
votes
4answers
2k views

Notation using “such that”

Is it correct to say "$a_t=\alpha:\alpha\in A_{\sigma}$" with the following meaning: $a_t$ is equal to $\alpha$ and $\alpha$ belongs to set $A_\sigma$.
3
votes
2answers
2k views

Set-builder notation: is there another symbol for “such that”?

My teacher is teaching us about sets, and he said that the '|', the ':' and the '\' symbols can be used to mean 'such that'. I'm certain of the first two, but I searched a little and couldn't find ...
2
votes
1answer
2k views

Predicate logic notation: where to put the parentheses, etc.

My math professor tends to write $\exists x\in\mathbf{X} \ni P(x)$. Is this a correct use of the such that symbol $\ni$? If not, what is the use of that symbol? Isn't it better to write $\exists x\in\...
1
vote
2answers
520 views

what does the inverse membership symbol means?

I know that the symbol $$ \in $$ stands for membership, but what does the symbol $$ \ni $$ stand for? Because I know that in the set membership, one symbol stands for subset and the other ones for ...
4
votes
2answers
80 views

Mathematical symbols for common phrases such as $\textit{for some}$ and $\textit{such that}$

I noticed that I use the phrases $\textit{for some}$ and $\textit{such that}$ a lot in pretty much every proof. Here is an example of the use of $\textit{for some}$: $\textit{The range of a function ...
4
votes
1answer
105 views

Is using the “contains” symbol $\ni$ frowned upon?

I am currently taking discrete math, and we have been learning several math symbols that we have used in our proof-writing assignments. Obviously, we have discussed the $\in$ symbol for inclusion in a ...
2
votes
0answers
42 views

What is the correct way to define a relation in an English sentence?

I would like to define several ordering relations. What is the correct way in an English sentence to phrase the sentence? I'm currently choosing between the following two awkward formulations. Let $...