Delta (Δ δ) in LaTeX
\delta and \Delta are the lowercase (δ) and uppercase (Δ) forms of the Greek letter delta in maths mode; uppercase Delta commonly denotes a finite change or difference, while lowercase delta denotes a small or infinitesimal one.
LaTeX command
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Uppercase Delta is one of the most recognisable maths symbols outside pure Greek-letter contexts, \Delta x almost universally means change in x, final value minus initial value, and it is also the standard symbol for a triangle in geometry and for the discriminant b^2 - 4ac of a quadratic.
Lowercase delta pairs with epsilon in real analysis's epsilon-delta definition of a limit, where delta bounds how close x must be to a point for f(x) to land within epsilon of the limit; it is also the Kronecker delta (\delta_{ij}, equal to 1 if i=j and 0 otherwise) and the Dirac delta function in physics and engineering.
The convention of Delta for a finite difference versus d or \partial for an infinitesimal one is worth keeping straight: \Delta x is a genuine, possibly large, difference used in difference quotients and numerical methods, while dx or \partial x are the calculus limits of that same idea as the change shrinks to zero.
Other forms
\deltalowercase delta\Deltauppercase delta (Δ)Examples
$\delta$lowercase delta inline
$\Delta$uppercase delta
$\Delta x = x_2 - x_1$delta as a finite difference
$\delta_{ij}$the Kronecker delta
$\forall \varepsilon > 0\, \exists \delta > 0$delta in the epsilon-delta limit definition
Tips and common mistakes
- Use
\Deltafor a finite change (\Deltax,\Deltat) and reserve d or\partialfor the calculus limit of that change as it shrinks to zero. - Delta has no var- variant, both
\deltaand\Deltaare the only standard forms. \Deltadoubles as the symbol for a triangle in plane geometry, for example\DeltaABC, distinct from its use as change in.- The discriminant of ax^2+bx+c is usually written
\Delta= b^2 - 4ac, don't confuse this with a change-in-x usage elsewhere in the same document. - The Kronecker delta
\delta_{ij}and the Dirac delta\delta(x) are both written with lowercase delta but behave very differently, one is a discrete indicator, the other a continuous generalised function.
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What is the LaTeX command for delta?
Lowercase delta is \delta (δ); uppercase delta is \Delta (Δ), for example and .
What does Delta mean in maths?
Most commonly change in, as in \Delta x meaning the difference between two values of x; it is also used for a triangle and for the discriminant of a quadratic.
What is the difference between delta and Delta?
Delta, uppercase, usually denotes a finite, often large, change or difference; delta, lowercase, usually denotes a small or infinitesimal quantity, an index-matching indicator, or appears in the epsilon-delta definition of a limit.
Is there a variant delta symbol?
No, delta has no var- form in standard LaTeX, unlike epsilon or phi.