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IntervalUnion—Wolfram Documentation

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IntervalUnion[interval1,interval2,…]

gives an interval containing the set of all points in any of the intervali.

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IntervalUnion

IntervalUnion[interval1,interval2,…]

gives an interval containing the set of all points in any of the intervali.

Details

  • The interval can be any of:
  • CenteredInterval[…]interval given by center and radius
    Interval[…]interval given by end points
  • If all the intervali are CenteredInterval[…], or at least one of the intervali is a nonreal interval, then the result will be a CenteredInterval[…] that contains all of the points in the intervali. Otherwise, the result will be the Interval[…] representing the set of all points in the intervali.

Examples

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Basic Examples  (2)

Combine intervals:

Wolfram Language code: IntervalUnion[Interval[{1, 3}], Interval[{2, 4}]]

Combine center-radius intervals:

Wolfram Language code: IntervalUnion[CenteredInterval[2 + 3I, 1 + I], CenteredInterval[1 + I, 2 + 2I]]

Scope  (4)

Combine disjoint intervals:

Wolfram Language code: IntervalUnion[Interval[{-2, 0}], Interval[{1, 4}]]

Combine disjoint real center-radius intervals:

Wolfram Language code: IntervalUnion[CenteredInterval[-1, 1 / 2], CenteredInterval[1, 1 / 2]]

Combine real intervals of different types:

Wolfram Language code: IntervalUnion[Interval[{-2, -1 / 2}, {1, 2}], CenteredInterval[0, 1 / 2]]

Combine intervals of different types, with at least one of them nonreal:

Wolfram Language code: IntervalUnion[Interval[{-2, -1 / 2}, {1, 2}], CenteredInterval[0, 1 / 2 + I / 2]]
Wolfram Research (1996), IntervalUnion, Wolfram Language function, https://reference.wolfram.com/language/ref/IntervalUnion.html (updated 2021).

Text

Wolfram Research (1996), IntervalUnion, Wolfram Language function, https://reference.wolfram.com/language/ref/IntervalUnion.html (updated 2021).

CMS

Wolfram Language. 1996. "IntervalUnion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/IntervalUnion.html.

APA

Wolfram Language. (1996). IntervalUnion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntervalUnion.html

BibTeX

@misc{reference.wolfram_2026_intervalunion, author="Wolfram Research", title="{IntervalUnion}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/IntervalUnion.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_intervalunion, organization={Wolfram Research}, title={IntervalUnion}, year={2021}, url={https://reference.wolfram.com/language/ref/IntervalUnion.html}, note=[Accessed: 14-November-2026]}