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downarrow

Represents a downward-pointing arrow symbol commonly used in mathematics and logic to indicate decreasing values or downward relationships.

Overview

Essential in mathematical notation for indicating decreasing sequences, downward limits, or vertical relationships between elements. Particularly valuable in:

  • Order theory to show decreasing relationships or descending chains
  • Set theory for denoting downward closure operations
  • Logic for representing implications or consequences
  • Statistics when indicating decreasing trends or values

Can be used both as a binary relation and as a standalone symbol, making it versatile for various mathematical contexts. Often paired with its upward counterpart for bidirectional relationships.

Examples

Showing a decreasing sequence or function.

f(x)↓0 as x→∞f(x) \downarrow 0 \text{ as } x \to \infty 
f(x) \downarrow 0 \text{ as } x \to \infty

Indicating a spin state in quantum mechanics.

∣↓⟩\left|\downarrow\right\rangle 
\left|\downarrow\right\rangle

Representing a downward trend in statistical analysis.

GDP growth: 3.2%↓2.1%\text{GDP growth: } 3.2\% \downarrow 2.1\% 
\text{GDP growth: } 3.2\% \downarrow 2.1\%