Many important mathematical ideas occur as pairs of opposites:
-2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),
bounded and unbounded, rational and irrational,
convergent and divergent, finite and infinite
Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:
horizontal and vertical, positive and negative,
open and closed, perpendicular and parallel
Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India; winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":
Epigrams by Rabindranath Tagore
I will close my door to shut out all possible errors.
"But how am I to enter in?" cried Truth.
"I have created this world," proclaims Time.
"And we have created you," the clocks chime.
The echo always mocks the sound -- to conceal that she is his debtor.
Death belongs to life as birth does, even as walking contains the raising of the foot as much as the laying of it down.
While God waits for his temple
to be built of love,
men bring stones.
Two of the epigrams above are from my copy of Rabindranath Tagore: An Anthology (St Martins Griffin, 1998) and the others are found here at Bartleby.com.