[permalink] [id link]

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

from
Wikipedia

## Some Related Sentences

** and Tarski's

** and theorem

__**__König's

__theorem__

**:**Colloquially

**,**

**the**sum of

**a**sequence of cardinals

**is**strictly less than

**the**product of

**a**sequence of larger cardinals

**.**

__**__If S

**is**

**a**

**set**of sentences of first-order logic

**and**B

**is**

**a**consistent subset of S

**,**then B

**is**included in

**a**

**set**that

**is**maximal among consistent subsets of S

**.**The special case where S

**is**

**the**

**set**of all first-order sentences in

**a**given signature

**is**weaker

**,**equivalent to

**the**Boolean prime ideal

__theorem__; see

**the**section " Weaker forms " below

**.**

__**__The Vitali

__theorem__on

**the**existence of non-measurable

**sets**which states that

**there**

**is**

**a**subset of

**the**real numbers that

**is**not Lebesgue measurable

**.**

__**__The Baire category

__theorem__about complete metric spaces

**,**

**and**its consequences

**,**such as

**the**open mapping

__theorem__

**and**

**the**closed graph

__theorem__

**.**

__**__Gödel's completeness

__theorem__for first-order logic

**:**

**every**consistent

**set**of first-order sentences has

**a**completion

**.**

__**__The numbers

**and**are not algebraic numbers ( see

**the**Lindemann – Weierstrass

__theorem__); hence they are transcendental

**.**

__**__More generally

**,**Rademacher's

__theorem__extends

**the**differentiability result to Lipschitz mappings

**between**Euclidean spaces

**:**

**a**Lipschitz

**map**ƒ

**:**U → R < sup > m </ sup >, where U

**is**an open

**set**in R < sup > n </ sup >,

**is**almost everywhere differentiable

**.**

__**__Artin reciprocity law

**,**

**a**general

__theorem__in number theory that provided

**a**partial solution to Hilbert's ninth problem

** and For

__**__

__For__example

**,**consider

**the**

**map**( which

**is**

**the**" realification " of

**the**complex square function ) where U

__**__

__For__some verbs in some languages

**,**

**the**difference

**between**perfective

**and**imperfective conveys an additional meaning difference ; in such cases

**,**

**the**two aspects are typically translated using separate verbs in English

**.**

__**__

__For__ohm – SI unit of electrical resistance ; formerly also used upside down () to represent mho

**,**

**the**old name for

**the**inverse of an ohm ( now siemens with symbol S ) used for electrical conductance

**.**

__**__

__For__instance

**,**when

**a**magazine claims that An MIT professor predicts that

**the**robotic era

**is**coming in 2050

**,**

**the**use of big-name " MIT " (

**a**world-renowned American university for

**the**advanced research in math

**,**science

**,**

**and**technology ) establishes

**the**" strong " credibility

**.**

__**__

__For__example

**:**One specific person may be identified by all of

**the**following identifiers

**:**Jane Smith ; Jane Elizabeth Meredith Smith ; Jane E

**.**M

**.**Smith ; Jane E

**.**Smith ; Janie Smith ; Janie ; Little Janie ( as opposed to her mother or sister or cousin

**,**Big Janie ); Aunt Jane ; Auntie Janie ; Mom ; Grandmom ; Nana ; Kelly's mother ; Billy's grandmother ; Ms

**.**Smith ; Dr

**.**Smith ; Jane E

**.**Smith

**,**PhD ;

**and**Fuzzy ( her jocular nickname at work ).

__**__Existence of additive inverse

**:**

__For__any integer

**a**

**,**

**there**exists an integer denoted by −

**a**such that

**a**+ (−

**a**)

2.070 seconds.