To write a “domain” correctly, you first need to be clear which kind of domain you mean: in math (domain of a function) or on the web (domain name like example.com). Both are common interpretations of “how to write domain.”

1. Writing the domain in math (functions)

In mathematics, the domain of a function is the set of all allowed input values (usually the xxx-values).

Common notations

  1. Interval notation (for continuous stretches of numbers)
 * Use round brackets (a,b)(a,b)(a,b) if endpoints are _not_ included.
 * Use square brackets [a,b][a,b][a,b] if endpoints _are_ included.
 * Use ∞\infty ∞ or −∞-\infty −∞ only with round brackets.
 * Examples:
   * All real numbers: (−∞,∞)(-\infty,\infty)(−∞,∞).

   * From 0 (included) to infinity: [0,∞)[0,\infty)[0,∞).

   * All real numbers except −4-4−4: (−∞,−4)∪(−4,∞)(-\infty,-4)\cup (-4,\infty)(−∞,−4)∪(−4,∞).
  1. Set-builder notation (for more “shaped” or restricted sets)
 * General form: {x∈R∣condition on x}\\{x\in \mathbb{R}\mid \text{condition on }x\\}{x∈R∣condition on x}.
 * The vertical bar ∣\mid ∣ means “such that,” ∈\in ∈ means “is in,” and R\mathbb{R}R is the real numbers.

 * Examples:
   * All real numbers except 0: {x∈R∣x≠0}\\{x\in \mathbb{R}\mid x\ne 0\\}{x∈R∣x=0}.

   * All real numbers with x>2x>2x>2: {x∈R∣x>2}\\{x\in \mathbb{R}\mid x>2\\}{x∈R∣x>2}.
  1. Listing values (discrete domains)
    • For a function defined only at specific points, you can list them:
      • Example: domain is {−5,0,5,10,15}\{-5,0,5,10,15\}{−5,0,5,10,15}.

How to find and then write the domain

  1. Identify the input variable (usually xxx).
  1. Check which inputs are not allowed, for example:
    • Denominator cannot be zero for rational functions.
 * Inside a square root, you usually must have the expression ≥0\ge 0≥0.
  1. Exclude those bad values.
  1. Write what remains using interval notation or set-builder notation.

Quick example (rational function):
If f(x)=1x−3f(x)=\dfrac{1}{x-3}f(x)=x−31​, then x−3≠0⇒x≠3x-3\ne 0\Rightarrow x\ne 3x−3=0⇒x=3. The domain is

  • Interval: (−∞,3)∪(3,∞)(-\infty,3)\cup (3,\infty)(−∞,3)∪(3,∞).
  • Set-builder: {x∈R∣x≠3}\{x\in \mathbb{R}\mid x\ne 3\}{x∈R∣x=3}.

2. Writing a domain name (web/URLs)

If by “write domain” you mean a website address (like myCoolSite.com), there are a few style and clarity tips.

Basic form

  • A domain name is the text people type to reach your site (for example: example.com).
  • When you write it in normal text, you usually omit “http://www” and just write:
    • example.com or domain.com.au/new-homes.

Readability and capitalization

  • For multi-word domains, capitalizing the first letter of each word makes them easier to read in text, especially in titles or print:
    • MyCoolSite.com instead of mycoolsite.com.
  • People often do this in marketing material and blog posts so readers can instantly see the word boundaries and remember the name.

SEO and URL structure

When writing the path part of a URL (after the domain) for articles or pages:

  • Include a relevant keyword.
  • Keep it descriptive and easy to read (use hyphens between words).
  • Keep it short, ideally about 3–5 words.
  • Example structure:
    • domain.com.au/new-homes — short, descriptive, hyphenated.

For choosing and writing the domain itself (the core name):

  • Use words that reflect your site’s topic or business. For a writing site, words like “write”, “writer”, “words” can help.
  • Make it easy to spell, pronounce, and remember.

3. Quick HTML table of key patterns

[3][1] [7][1] [2] [6][8] [2]
Context How to write domain Example
Math – interval notation Use brackets/parentheses, include unions if needed. $$[0, \infty)$$, $$(-\infty, -4) \cup (-4, \infty)$$.
Math – set-builder $$\\{x \in \mathbb{R} \mid \text{condition}\\}$$. $$\\{x \in \mathbb{R} \mid x \ne 0\\}$$.
Web – plain domain Write without protocol, avoid “www” unless needed. `domain.com.au`.
Web – readable domain in text Capitalize each word for clarity. `MyCoolSite.com`, `FollowSteph.com`.
Web – URL path Use short, keyword-rich, hyphen- separated words. `domain.com.au/new-homes`.

4. If you meant “trending topic / forums”

“Domain” also shows up in forum discussions about:

  • Picking a niche/domain for writing or blogging (e.g., “Choose a domain relevant to your content-writing service and include words like ‘write’ or ‘words’.”).
  • Branding and readability tricks like capitalizing each word of your domain in posts and on business cards.

TL;DR:

  • For math, write the domain using interval notation like [0,∞)[0,\infty)[0,∞) or set-builder notation like {x∈R∣x≠0}\{x\in \mathbb{R}\mid x\ne 0\}{x∈R∣x=0}.
  • For websites, write domain names clearly (often capitalizing each word in text) and use short, meaningful, hyphenated paths for URLs.

Information gathered from public forums or data available on the internet and portrayed here.