bijection

• “You can make each point have measure 1/2, for example, or assign whatever positive weights you like to each point (such measures are in bijection with functions from your base set to the positive reals).”

  Matthew Yglesias » Null Set Blogging

• “Ω (mˆ) says that there is no bijection between the natural numbers and mˆ.”

  Skolem's Paradox

• “If asked about the phrase “is a bijection,” she will go on to talk about collections of ordered pairs satisfying certain nice properties, and if asked about the term”

  Skolem's Paradox

• “If we are willing make the further assumption that it only takes one bijection to one such instance of the power set of ω to render the power set itself “absolutely” countable, then we can understand the Skolemite's strong claim about absolute countability.”

  Skolem's Paradox

• “(A set is reflexive iff it is equipollent to one of its proper subsets; and two sets are equipollent with one another iff there exists a bijection, i.e., a one-to-one correspondence, between them.)”

  Fictionaut: Slices of Matisse

• “Dedekind also provided a proof of the Cantor-Bernstein Theorem (that between any two sets which can be embedded into each other one-to-one there exists a bijection, so that they have the same cardinality), another basic result in the modern theory of transfinite cardinals.”

  Dedekind's Contributions to the Foundations of Mathematics

• “On the other hand, in Mirimanoff's 1917a there is a remarkable use of Burali-Forti's paradox which suggests a necessary condition for set-hood in terms of size, viz., if a collection is in bijection with the set of all ordinals, then it does not exist as a set.”

  Paradoxes and Contemporary Logic

• “The bijection we have just observed can now be stated as”

  Algebra

• “F is a bijection from W onto the set of all maximal consistent sets of facts.”

  Facts

• “F is a bijection from W onto the set of all conjunctively complete sets of facts;”

  Facts

Show 10 more examples...