notation - What does := mean? - Mathematics Stack Exchange
What does “In” stand for, and how does it pertain to solving this equation?
Guys what does the ∑ symbol mean in math
What does "in" mean in math?
Videos
It is borrowed from computer programming: it means that the item on the left hand side is being defined to be what is on the right hand side. For example,
means that 
is defined to be 
.
This is different from, say, writing
where we are saying that the two sides are equal, but we are not defining "1" to be the expression "
".
Basically, some people think that there should be notational difference between saying "I define blah to be equal to blankety" and saying "blah is equal to blankety". So they use := for the first and = for the latter. Usually, it is clear from context which of the two uses of the equal sign is intended (often because of signal words like "Let", "We define", etc.)
I think the Bourbaki used it first.. not sure.. I know physicists use 
I'm trying to use a delta-v formula, which is
Delta-V = Isp9.81ln(m1/m2)
But I have no idea what in is. Thanks in advance for the answer!
And what it is used for?
Hi everybody! I'm currently working through Linear Transformations and Matrices by F. A. Ficken and while I generally understand what's happening in each subsection, I keep getting stuck on the questions because I don't know what they're asking me to do. The biggest issue is that I don't know what it means when a question asks me to "define" something. I feel like I'm missing something major because I understood the section on recursive definitions and was able to "define" sequences based on that understanding but then questions started asking me to define a given equation such as a₀ = b and I have no idea what it wants me to do. Another question said to define the symbols that denote '1 choose 0' = 1 and '1 choose 1' = 1, I'm also completely lost there.
I feel like my issue is that I'm not in a math class with a prof who can explain these things to me but I really want to learn on my own. I tried looking for video lectures but I can't figure out what to search to get what I'm looking for.
Thanks so much in advance for any help anyone can provide.
Edit: here's a question I'm stuck on, https://imgur.com/a/2xs6HME
$\in$ means '(is) an element of a set'
For instance, 'Let $a\in A$' means 'Let $a$ be an element of $A$'
http://en.wikipedia.org/wiki/Element_(mathematics) might help you too
∈ (mathematics) means that it is an element in the set of… For eg...x ∈ ℕ denotes that x is within the set of natural numbers.
The relation "is an element of", also called set membership, is denoted by the symbol "∈". Writing {\displaystyle x\in A} x\in A means that "x is an element of A". Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". The expressions "A includes x" and "A contains x" are also used to mean set membership, however some authors use them to mean instead "x is a subset of A".
Another possible notation for the same relation is {\displaystyle A\ni x,} A\ni x, meaning "A contains x", though it is used less often. The negation of set membership is denoted by the symbol "∉". Writing {\displaystyle x\notin A} x\notin A means that "x is not an element of A".
I do avoid using this phrase in all of my math classes. Not that I've ever thought of it as a particular goal, but I would want to reserve the word "term" to specify an addend.
In your first example, I would specify, "Write a formula using the variable $x$". In your second example, I specify, "Solve the following equation for $y$" (end of direction), having previously defined "solving" as isolating the indicated variable on one side.
I had similar problems with the phrase "such that" as taught in set-builder notation. Still--40 years later--I don't like the expression "such that." It's just not a phrase I would ever use naturally. I learned to read (in my head) the vertical bar in set builder notation as "where."
I haven't experienced the problem you described with any students I've taught. But I might apply the same solution: give your students a number of equivalent expression they can substitute in their heads. For example, "in terms of x" = "using units of x" = "where the variable x appears in the answer." For the students that do seem to grasp concept, ask them to suggest equivalent phrases.
Three other observations: 1) The word "term" has at least two meanings. One meaning is a part of a polynomial that is expressed without addition or subtraction operators. But a second meaning is "a specific word or expression," as in "vocabulary terms." The phrase "in terms of" uses the 2nd meaning. If you have emphasized the first meaning with your students, it may be helpful to state explicitly that you're using the 2nd meaning.
2) I understand this may be an artifact of typing your question, but I found your example "x apples" a little confusing myself. In this case, x is a unitless number, and the "units" are apples. So asking for the answer "in terms of x" seems like you're asking for an answer "in terms of a unitless number." I don't think you mean "in terms of x." In that particular example, I think you mean "in terms of apples" = "using units of 'apples'."
3) Have your students been exposed to dimensional analysis (a.k.a. unit analysis) in your course or previous ones? The concept of a conversion factor is closely related to this question. Your students are probably used to converting between inches and centimeters or other units of measure. Perhaps you can give them a serious of word problems involving unit conversion, and the word problems can use the phrase "in terms of." This may help get them accustomed to the meaning of the phrase. For example, "Express the capacity of a 10 gallon gas tank in terms of liters."