The symbol ≜, also known as "delta equal to" or "equal-delta," is a mathematical symbol used to denote a definition.
Understanding the Symbol ≜
The symbol ≜ is formally represented in Unicode as 'DELTA EQUAL TO' (U+225C). It serves as a shorthand notation, primarily in mathematics and physics, to indicate that a particular term is being defined or is equal to something by definition.
Formal Definition
When you see the notation t ≜ m, it generally means:
- "t is defined to be m."
- "t is equal by definition to m."
Often, this definition is valid under specific conditions or contexts. It's a crucial distinction from regular equality, which implies a relationship derived from a calculation or established fact rather than a stipulation.
Key Uses of ≜
- Defining New Variables or Terms: It allows you to introduce a new symbol and declare what it represents.
- For instance, y ≜ 2x + 1 means we are defining y to be the expression 2x + 1.
- Representing Specific Cases: x ≜ 5, often in the context of examples, can be used to fix the value of variable x to 5.
- Clarifying Context: It helps in maintaining mathematical rigor and clarity when a new symbol or term is introduced.
Comparison with Standard Equality (=)
The standard equality symbol (=) generally denotes a relationship that holds true based on prior rules or computations. In contrast, ≜ defines a relationship, stating that, from now on, one expression is to be taken as equivalent to another by definition.
| Symbol | Meaning |
|---|---|
| = | Standard equality |
| ≜ | Equality by definition or defined as |
Origin of the Symbol ≜
While the exact origin of this symbol and the person who first used it remains elusive, it has gained common usage in mathematics, especially in logic, for stating definitions clearly.
Practical Example
Let's say you define the speed of an object as v, its distance traveled as d, and the time taken as t. If you define speed in terms of the other variables:
- v ≜ d/t. This equation means the speed v is defined as the distance traveled divided by time taken. This is not derived from other principles; it is set as a definition.
Conclusion
The symbol ≜ is a mathematical symbol specifically used for definition. It indicates that the term on the left side is defined to be equal to the expression on the right, often within a specific context. Understanding the use of ≜ is essential for accurately interpreting mathematical and scientific notations.
