Cantor set

American  

noun

Mathematics.

1. the set obtained from the closed interval from 0 to 1 by removing the middle third from the interval, then the middle third from each of the two remaining sets, and continuing the process indefinitely.

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Etymology

Origin of Cantor set

After G. Cantor

Example Sentences

And it’s not just because we usually think of the Cantor set as living in two dimensions and Antoine’s necklace as living in three.

From Scientific American • Jul. 8, 2018

Any space with these properties can be called a Cantor set, and in some sense, there's nothing special about the middle-thirds construction.

From Scientific American • Jul. 8, 2018

I feel a little weird saying the Cantor set, though, because for the space I’m writing about today, it makes more sense to call it a Cantor set.

From Scientific American • Jul. 8, 2018

For every point x in the Cantor set, we have a line connecting x to p.

From Scientific American • Jun. 20, 2015

In Cantor’s leaky tent, the countably many endpoints of the Cantor set are paired with the countably many rational points on the line to p.

From Scientific American • Jun. 20, 2015