The Mathematical Symbol "Because (∵)"
The ∵ Symbol in Mathematics: Expressing Reasoning
The ∵ symbol in mathematics stands for "Because". It serves as a concise way to denote the reason or justification for a certain statement or result. Its primary role is to provide a bridge between a given statement and its underlying reason. In this article, we'll discuss two main scenarios where the ∵ symbol finds its application, accompanied by two examples for each context.
1. Mathematical Proofs and Derivations
In mathematical proofs and derivations, the ∵ symbol is used to logically connect a statement to its rationale.
- Example 1: If a student claims that \( 2 + 2 = 4 \) ∵ it is an elementary arithmetic fact, they're using the symbol to link their statement with its reason.
- Example 2: In algebra, one might note that \( x^2 \geq 0 \) for all real \( x \) ∵ the square of any real number is non-negative.
2. Providing Clarifications
Another common use of the ∵ symbol is to provide clarifications or further details on a given statement or scenario.
- Example 1: A mathematician might argue that a particular mathematical method is preferred ∵ it offers faster computational speeds.
- Example 2: In statistical studies, a researcher could state that a particular data set was chosen ∵ it is more representative of the general population.
In summary, the ∵ symbol offers a succinct way to express reasoning in mathematical contexts. Its use enhances clarity and aids in bridging the gap between statements and their justifications, thereby enriching the reader's understanding.
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Codes for the ∵ Symbol
| The Symbol | ∵ | |
| Alt Code | Alt 8757 | |
| HTML Code | ∵ | |
| HTML Entity | ∵ | |
| CSS Code | \2235 | |
| Hex Code | ∵ | |
| Unicode | U+2235 |
How To Insert the ∵ Symbol
(Method 1) Copy and paste the symbol.
The easiest way to get the ∵ symbol is to copy and paste it into your document.Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.
(Method 2) Use the "Alt Code."
If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8757. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)(Method 3) Use the HTML Decimal Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ∵</b> | My symbol: ∵ |
(Method 4) Use the HTML Entity Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ∵</b> | My symbol: ∵ |
(Method 5) Use the CSS Code (for webpages).
| CSS and HTML Text | Output |
|---|---|
|
<style> span:after { content: "\2235";} </style> <span>My symbol:</span> | My symbol: ∵ |
(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).
| HTML Text | Output |
|---|---|
| <b>My symbol: ∵</b> | My symbol: ∵ |
| JavaScript Text |
|---|
|
const x = "0x"+"E9" ctx.fillText(String.fromCodePoint(x), 5, 5); |
| Output |
∵ |
(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).
The Unicode for ∵ is U+2235. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:| Type | Output |
|---|---|
| 2235 [Hold down Alt] [Press x] | ∵ (The 2235 turns into ∵. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u2235" document.write("My symbol: " + str) | My symbol: ∵ |