135
votes
Accepted
Does notation ever become "easier"?
As others have pointed out, it gets much better if that's your first semester. But in my experience, there is not much relief between, say, years 2 and 4 of your studies. Sure, you get more mature, ...
- 7,730
127
votes
Accepted
Is there a symbol for "taking a derivative of something"?
You would denote the derivative of $5x^3+7x^2+4x+9$ as
$$\frac{d}{dx}(5x^3+7x^2+4x+9)$$
That is the only notation I've ever seen unless the expression is expressed as a function.
- 40.1k
115
votes
Accepted
Example of a very simple math statement in old literature which is (verbatim) a pain to understand
Here's Proposition 2 from Book 5 of Euclid's Elements:
If a first magnitude and a third are equal multiples of a second and a fourth, and a fifth and a sixth are equal multiples of the second and ...
- 25.7k
106
votes
Accepted
Are there dictionaries in math?
A dictionary is just a function $\mathrm{Dict}\colon \mathrm{Keys} \rightarrow \mathrm{Values}\cup\{\epsilon\}$ where $\epsilon$ is a "null character" with the understanding that $\epsilon\notin\...
- 25.3k
87
votes
Accepted
Is there a math expression equivalent to the conditional ternary operator?
From physics, I'm used to seeing the Kronecker delta,$$
{\delta}_{ij}
\equiv
\left\{
\begin{array}{lll}
1 &\text{if} & i=j \\
0 &\text{else}
\end{array}
\right. _{,}
$$and I think people ...
- 1,504
85
votes
Accepted
Mathematical symbol for 'slightly greater than'?
More often it is used as $b=a+\epsilon$ where $\epsilon$ normally stands for a small positive quantity. That provides b slightly greater than a. Similarly $-\epsilon$ for slightly below.
- 5,223
83
votes
Accepted
What does the mysterious constant marked by C on a slide rule indicate?
I found the answer by googling "slide rule markings"! It took me straight to the Glossary of the International Slide Rule Museum, which gives C its own entry:
C - Gauge mark found on the C and D ...
- 65.6k
81
votes
Accepted
What are good "math habits" that have improved your mathematical practice?
I think this is a great question and you've already made an important step in addressing the problem - realizing that you are not satisfied with your math working process and searching for ways to ...
- 66.2k
80
votes
Why write ten as $10$ and not as $00$
The point of decimal notation is not just to assign each number a "code" - it has an attached meaning.
When we write a decimal expression $$a_na_{n-1}...a_2a_1a_0,$$ what we mean is $$a_n10^n+a_{n-1}...
- 251k
77
votes
Accepted
Why does "Turn! Turn! Turn!" equal 241217.524881?
It appears that Google search uses the following syntax for conversions between different units or currencies: target_unit! <expression> (Though I can't find ...
- 833
73
votes
Accepted
Notation: Vector contains an element equal to 0
It's best to write it in words:
$$
f(v)
=
\begin{cases}
1&\text{when at least one component of $v$ is zero}\\
0&\text{otherwise}.
\end{cases}
$$
This is perfectly valid mathematical notation.
...
- 26k
68
votes
Mathematical symbol for 'slightly greater than'?
Perhaps:
$$\lt_\epsilon\quad\gt_\epsilon\quad\lt^\epsilon\quad\gt^\epsilon$$
using the idea that $a\lt^\epsilon b$ means $a+\epsilon=b$, where $\epsilon\gt0$.
- 21.9k
68
votes
Abusing mathematical notation, are these examples of abuse?
The example you've given of a function is not an abuse. $x$ is instead shorthand for $\pi_1(t)$ and $y$ is shorthand for $\pi_2(t)$ and $(x,y)$ is shorthand for $t$.
$g \in G$ is a very minor abuse, ...
- 36.5k
68
votes
Accepted
How do I make proofs with long formulae more readable without sacrificing clarity?
Main suggestion
Instead of
We want to show $\def\p{\phi}\def\q{\psi}\def\s{\vDash_{\tiny\text{PL}}}\def\ns{\nvDash_{\tiny\text{PL}}}\p_1,\,\p_2,\,\ldots,\,\p_n\s\q$ iff $\s\p_n\to(\p_{n-1}\to(\cdots\...
65
votes
Is there a math expression equivalent to the conditional ternary operator?
The expression b + (c > 0 ? 1 : 2) is not a ternary operator; it is a function of two variables. There is one operation that results in $a$. You can certainly ...
- 379k
63
votes
What is the reasoning behind this exponents question?
Unlike addition and multiplication, exponentiation is not associative:
$(a+b)+c=a+(b+c)$
$(a\times b)\times c=a\times (b\times c)$
but
($a$^$b$)^$c\ne a\!$^($b$^$c$), more commonly written as: $\...
- 28k
61
votes
Is an infinite composition of bijections always a bijection?
We shouldn't expect limits (of any sequence of functions) to preserve injectivity, since limits can change strict inequalities into nonstrict inequalities.
For a concrete counterexample, consider each ...
- 84.8k
60
votes
How to write zero in the unary numeral system
You do something like this:
Sneaky, no?
"Unary" is just a tally-mark system, not a really full-fledged numeral system. You represent Zero by not representing any quantity at all.
One Apple: |
...
- 758
56
votes
Accepted
Weird large K symbol
It is the notation for a continued fraction.
In general:
$$b_0 + \underset{k=1}{\overset{\infty}{\large{\mathrm K}}} \left(\frac{a_k}{b_k}\right)=b_0 + \cfrac{a_1}{b_1 + \cfrac{a_2}{b_2 + \cfrac{a_3}{...
- 15.5k
56
votes
Accepted
Why is union sign not allowed to denote intervals of function increasing?
The function is decreasing (not increasing, as you said) on each of those three intervals separately. But it is not decreasing on their union because, for example, $f(5)>f(0)$.
Consider a similar ...
56
votes
Is the percentage symbol a constant?
Isn't the percentage symbol actually just a constant with the value $0.01$?
No. If it were, all of the following would be valid constructs:
$$
30+\%\,50=30.5\\
90\,\%\,\mathrm{cm}=0.9\,\mathrm{cm}\\
...
- 685
55
votes
Example of a very simple math statement in old literature which is (verbatim) a pain to understand
See Tartaglia's formula for the cubic equation, which is a poem with over 20 lines. (http://www.maa.org/press/periodicals/convergence/how-tartaglia-solved-the-cubic-equation-tartaglias-poem)
...
- 19.9k
52
votes
Notation for an interval when you don't know which bound is greater
One possibility is $\operatorname{Conv}(a,b)$: the convex hull of $a$ and $b$. Maybe this should really be $\operatorname{Conv}(\{a,b\})$, but I think it is forgivable to omit the curly braces - or ...
- 146k
52
votes
Is there a math expression equivalent to the conditional ternary operator?
In Concrete Mathematics by Graham, Knuth and Patashnik, the authors use the "Iverson bracket" notation: Square brackets around a statement represent $1$ if the statement is true and $0$ otherwise. ...
- 4,368
49
votes
Accepted
Difference between $⊂$ and $⊆$?
If the book distinguishes between $\subset$ and $\subseteq$, then most likely the former symbol denotes proper inclusion, so $\{0\}\subset\{0\}$ is false. The latter symbol instead will denote ...
- 241k
47
votes
Accepted
What is the mathematical notation for rounding a given number to the nearest integer?
I have seen $\lfloor x \rceil$. It must have been in the context of math olympiads, so I can't point to a book that uses it. Wikipedia suggest this notation, among others: nearest integer function.
...
- 26.6k
45
votes
Is there a symbol for "taking a derivative of something"?
A common choice of notation is $D_{x}(5x^3 + 7x^2 + 4x + 9)$. The subscript indicates the variable with respect to which one is differentiating.
- 31.1k
45
votes
Notation for an interval when you don't know which bound is greater
Assuming you're meaning the closed interval for the notation I'm going to write, something that will always work is
$$[\min\{a,b\}, \max\{a,b\}]$$
Another possibility is
$$[a,b] \cup [b,a]$$
But ...
- 6,383
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