Paradox (literature)
Paradox, however, is essential to the structure and being of the poem. In "The Well Wrought Urn" Brooks shows that paradox was so essential to poetic meaning that paradox was almost identical to poetry. According to literary theorist Leroy Searle, Brooks' use of paradox emphasized the indeterminate lines between form and content. "The form of the poem uniquely embodies its meaning," and the language of the poem "affects the reconciliation of opposites or contraries." While irony functions within the poem, paradox often refers to the meaning and structure of the poem and is thus inclusive of irony. This existence of opposites or contraries and the reconciliation thereof is poetry and the meaning of the poem.
Hausdorff paradox
The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff. It involves the sphere "S" (a 2-dimensional sphere in "R"). It states that if a certain countable subset is removed from "S", then the remainder can be divided into three disjoint subsets "A", "B" and "C" such that "A", "B", "C" and "B" ∪ "C" are all congruent. In particular, it follows that on "S" there is no finitely additive measure defined on all subsets such that the measure of congruent sets is equal (because this would imply that the measure of "B" ∪ "C" is simultaneously 1/3 and 2/3 of the non-zero measure of the whole sphere).