Intereting Posts

different possible definitions of the exterior derivative?
How prove this inequality $(a+b+c+d+e)^3\geq9(2abc+abd+abe+acd+ade+2bcd+bce+bde+2cde),$
What's the probability of a an outcome after N trials, if you stop trying once you're “successful”?
Groups with only one element of order 2
sum of logarithms
Computational complexity of least square regression operation
Set theory: difference between belong/contained and includes/subset?
For which integers $a,b,c,d$ does $\frac{a}{b}+\frac{c}{d} = \frac{a+c}{b+d}$?
Eigenfunction of the Fourier transform
Decomposition of finitely generated graded modules over PID
A generalization of IMO 1983 problem 6
Erdős-Straus conjecture
Why does cancelling change this equation?
What is the rank of COCHIN
Proof that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$

This could be a trivial question, but what is exactly the difference of between these two expressions? Am I correct to state the both interchangeably whenever I need to express the approximation of pi? I’m bit confused as here it states pi can be express by ≒ as it’s not a rational number, but pi can also be expressed by a series (asymptotic), so it should be ≈ as well.

```
π ≈ 3.14..
π ≒ 3.14..
```

- Are “if” and “iff” interchangeable in definitions?
- Nested solutions of a quadratic equation.
- Can a function be increasing *at a point*?
- Why does the definition of an open subscheme / open immersion of schemes allow for an “extra” isomorphism?
- Two definitions of $\limsup$
- Why can't we define more elementary functions?
- A series to prove $\frac{22}{7}-\pi>0$
- Why is the expression $\underbrace{n\cdot n\cdot \ldots n}_{k \text{ times}}$ bad?
- Is function $f:\mathbb C-\{0\}\rightarrow\mathbb C$ prescribed by $z\rightarrow \large \frac{1}{z}$ by definition discontinuous at $0$?
- Definition of adjoint functor similar to the definition of homotopy equivalence?

Any mathematical notation is ok as long as it is common knowledge in your community. For instance, I believe I fully understand the meaning of the $\approx$ symbol. However, I haven’t ever seen the second symbol you provided.

To be on the sure side you should provide a definition of any relation symbol you don’t consider to be common knowledge. This may happen as a short remark (“…, where $\approx$ denotes …”) or maybe as a table of the used symbols in the front matter of your work. As with any definition in mathematics, there is no right or wrong in the symbol/notion/etc. you use, only proper or unsound definitions.

Also: When in doubt, use the symbol that is used more commonly in the standard textbooks of your field. There is no benefit in being avant-garde at notation.

While it is certainly true that with the proper definition there is now ‘wrong’ notation, perhaps it should be mentioned that some notation is more suggestive and/or easier to work with than others, e.g. Arabic numeral vs. Roman numerals, the various symbols for the derivative, and countless others. The actual symbols are arbitrary, but good notation can certainly promote the flow of ideas more easily.

Also, do I remember correctly that Feynman gave up trying to invent more efficient notation for simple math when he was quite young because nobody could understand what he was doing?

A good notation has a subtlety and suggestiveness which at times make it almost seem like a live teacher.

–Bertrand Russell

The first one with the equal sign and the two dots is actually the Japanese version….the bottom one is more common in the West.

- Computing the $n^{\textrm{th}}$ permutation of bits.
- Surreal and ordinal numbers
- Ordered Pair Formal Definition
- Prove the inequality $n! \geq 2^n$ by induction
- Evaluate $\int_{|z|=r}^{}\frac{\log\ z}{z^2+1}dz$ where $r>0$
- Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
- Find all positive integers $n$ s.t. $3^n + 5^n$ is divisible by $n^2 – 1$
- Does Hartshorne *really* not define things like the composition or restriction of morphisms of schemes?
- solve $x^2 – 25 xy + y^2 = 1$ does it have a solution?
- Does Pi contain all possible number combinations?
- What is a good book for learning Stochastic Calculus?
- Continuous increasing bounded function, derivative
- Number of non decreasing sequences of length $M$
- Rearrangements of absolutely convergent series
- How many values does the expression $1 \pm 2 \pm 3 \pm \cdots \pm n$ take?