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BinaryDistance[u,v]

gives the binary distance between vectors u and v, equal to 0 if they are identical and 1 otherwise.

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BinaryDistance

BinaryDistance[u,v]

gives the binary distance between vectors u and v, equal to 0 if they are identical and 1 otherwise.

Details

Examples

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Basic Examples  (2)

Binary distance between numeric vectors:

Wolfram Language code: BinaryDistance[{1, 2, 3}, {2, 4, 6}]

Binary distance between two identical symbolic vectors:

Wolfram Language code: BinaryDistance[{a, b, c}, {a, b, c}]

Scope  (4)

Compute distance between arbitrary expressions:

Wolfram Language code: BinaryDistance["text", {1, 2, 3}]

Binary distance between numeric vectors of different length:

Wolfram Language code: BinaryDistance[{1, 2, 3}, {1, 2}]

Binary distance between symbolic inputs:

Wolfram Language code: BinaryDistance[a, b]

Binary distance between two vectors:

Wolfram Language code: BinaryDistance[{a, b, c}, {x, y, z}]

Applications  (1)

Cluster data using BinaryDistance:

Wolfram Language code: FindClusters[{{2, 3}, {5, 10}, {4, 5}, {2, 3}}, DistanceFunction -> BinaryDistance]

Properties & Relations  (3)

Approximate numbers may be considered identical:

Wolfram Language code: BinaryDistance[1, 1.]

BinaryDistance is effectively related to Equal:

Wolfram Language code: BinaryDistance[1, 1.] == Boole[Not[1 == 1.]]

Demonstrate the triangle inequality:

Wolfram Language code: d1 = BinaryDistance[{a, b}, {a, c}]
Wolfram Language code: d2 = BinaryDistance[{a, c}, {d, c}]
Wolfram Language code: d3 = BinaryDistance[{a, b}, {d, c}]
Wolfram Language code: Simplify[d3 ≤ d1 + d2]

Possible Issues  (1)

The returned distance may not be completely simplified:

Wolfram Language code: BinaryDistance[{Gamma[x] Gamma[1 - x]}, {π Csc[π x]}]

Simplify the result further:

Wolfram Language code: FullSimplify[%]
Wolfram Research (2015), BinaryDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/BinaryDistance.html.

Text

Wolfram Research (2015), BinaryDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/BinaryDistance.html.

CMS

Wolfram Language. 2015. "BinaryDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BinaryDistance.html.

APA

Wolfram Language. (2015). BinaryDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BinaryDistance.html

BibTeX

@misc{reference.wolfram_2026_binarydistance, author="Wolfram Research", title="{BinaryDistance}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/BinaryDistance.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_binarydistance, organization={Wolfram Research}, title={BinaryDistance}, year={2015}, url={https://reference.wolfram.com/language/ref/BinaryDistance.html}, note=[Accessed: 13-June-2026]}