[permalink] [id link]

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

from
Wikipedia

## Some Related Sentences

** and Hausdorff

** and maximal

__**__Zorn's lemma

**:**Every non-empty

**partially**

**ordered**

**set**

**in**which

**every**chain ( i

**.**e

**.**

**totally**

**ordered**

**subset**) has an upper bound contains at least one

__maximal__element

**.**

__**__Tukey's lemma

**:**Every non-empty collection of finite character has

**a**

__maximal__element with respect to inclusion

**.**

__**__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

**.**

__**__Referring to diplomas and degrees

**:**cum laude ( with praise ), magna cum laude ( with great praise ); maxima cum laude ( with

__maximal__praise ); summa cum laude ( with highest praise ); egregia cum laude ( with outstanding praise )

__**__Maximal planar graphs are sometimes called triangulations

**,**and

**a**

__maximal__planar supergraph of

**a**graph G may be called

**a**triangulation of G

**.**

__**__These two concepts come together

**in**strangulated graphs

**,**which include both

__maximal__planar graphs and chordal graphs

**.**

** and principle

__**__Microevolution

**:**species — speciation — adaptation — selection — natural selection — directional selection — sexual selection — genetic drift — sexual reproduction — asexual reproduction — colony — allele frequency — neutral theory of molecular evolution — population genetics — Hardy-Weinberg

__principle__

__**__The segmented DAC

**,**which combines the thermometer-coded

__principle__for the most significant bits and the binary-weighted

__principle__for the least significant bits

**.**

__**__

**In**the mid-1950s

**,**

**a**second land reform during the Great Leap Forward compelled individual farmers to join collectives

**,**which

**,**

**in**turn

**,**were grouped into People's communes with centrally controlled property rights and an egalitarian

__principle__of distribution

**.**

__**__Some

**,**including the leadership of the Society of St Pius X

**,**hold that it

**is**

**in**

__principle__valid as

**a**sacramental rite but maintain that the revisions

**in**the liturgy are displeasing to God

**,**and that it

**is**often celebrated improperly to the extent of being sacramentally invalid

**.**

__**__Some

**,**including many sedevacantists

**,**see it as categorically invalid

**in**

__principle__and entirely unacceptable

**.**

__**__What are ( necessary and sufficient ) conditions for consistency of

**a**learning process based on the empirical risk minimization

__principle__?

__**__Stalin

**ordered**that the persecution be enhanced

**:**NKVD

**is**" four years late "

**in**crushing the opposition

**,**according to his

__principle__of " aggravation of class struggle "

__**__the Government decision of December 2002 to agree

**in**

__principle__to the provision of additional resources was made contingent on the outcome of the review

**,**and so had proved meaningless

**.**

__**__T31 / M5A2-Similar

**in**

__principle__to the M3A2

**,**

**a**vehicle developed by the US Ordnance Department to combine the production of the M5 and M9 into

**a**single vehicle

**.**

** and any

__**__The Serbians use word " cifra ", which refers to

__any__number

**.**Besides " cifra ", they use word " broj ".

__**__

**In**particular

**,**the cofinality of

__any__nonzero finite ordinal

**,**or indeed

__any__finite directed

**set**

**,**

**is**1

**,**since such sets have

**a**greatest element

**.**

__**__

**In**power engineering

**,**

**a**" bus "

**is**

__any__graph node of the single-line diagram at which voltage

**,**current

**,**power flow

**,**or other quantities are to be evaluated

**.**

__**__Old Believings It was believed that

**in**England

**in**the 14th century

**,**that plains of

__any__kind

**is**where the dead wandered searching for their revenge

**.**

__**__This could be

__any__position

**in**which the speaker — whether an acknowledged expert on the subject

**,**or an acquaintance of

**a**person who experienced the matter

**in**question — knows about the topic

**.**

__**__Sodium chloride ( table salt ) or

__any__other salt

**in**water forms an electrolyte

**:**When dissolving

**,**salt dissociates into ions

**.**

__**__

**In**the UK

**,**

**a**protective trust

**is**

**a**life interest which terminates on the happening of

**a**specified event such as the bankruptcy of the beneficiary or

__any__attempt by him to dispose of his interest

**.**

__**__San Francisco elects City Supervisor Harvey Milk

**,**the first openly gay elected official of

__any__large city

**in**the U

**.**S

**.**

__**__British Prime Minister Neville Chamberlain states

**in**the House of Commons that

__any__German attack on France will be automatically considered an attack on Britain

**.**

__**__The Western Allies flatly reject

__any__offer of surrender by Germany other than unconditional on all fronts

**.**

__**__American Civil War

**:**The U

**.**S

**.**House unanimously passes

**a**resolution guaranteeing non-interference with slavery

**in**

__any__state

**.**

__**__A decision by the Supreme Court of the United States states that the power of the federal government

**is**greater than

__any__individual state

**.**

__**__The Naval Defence Act dictates that the fleet strength of the British Royal Navy must be equal to that of at least

__any__two other countries

**.**

__**__Pakistan Navy raids Indian coasts without

__any__resistance

**in**Operation Dwarka

**,**Pakistan celebrates Victory Day annually

**.**

__**__Brisbane receives

**a**daily rainfall of 465 millimetres –

**a**record for

__any__Australian capital city

**.**

__**__Pen Hadow becomes the first person to walk alone

**,**without

__any__outside help

**,**from Canada to the North Pole

**.**

0.964 seconds.