{"id":80,"date":"2009-10-15T19:11:39","date_gmt":"2009-10-15T16:11:39","guid":{"rendered":"http:\/\/ramuuns.id.lv\/blog\/?p=80"},"modified":"2009-10-16T11:39:20","modified_gmt":"2009-10-16T08:39:20","slug":"skaitlu-teorijas-elementi","status":"publish","type":"post","link":"https:\/\/ramuuns.com\/blog\/2009\/10\/15\/skaitlu-teorijas-elementi\/","title":{"rendered":"Skait\u013cu teorijas elementi"},"content":{"rendered":"

V\u0113lviens ieraksts no s\u0113rijas “lekciju pieraksti”<\/p>\n

2.1. Re\u0101lo skait\u013cu \u012bpa\u0161\u012bbas<\/p>\n

Aksiom\u0101tiska def.<\/p>\n

\u012apa\u0161\u012bbu grupas<\/p>\n

\n\n\n<\/col>\n<\/col>\n<\/colgroup>\n\n\n\n\n\n\n
I<\/td>\n<<\/td>\n<\/tr>\n
II<\/td>\n+<\/td>\n<\/tr>\n
III<\/td>\n*<\/td>\n<\/tr>\n
IV<\/td>\nArhim\u0113da \u012bpa\u0161.<\/td>\n<\/tr>\n
V<\/td>\nNep\u0101rtraukt\u012bbas \u012bpa\u0161\u012bba<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

I R <\/strong> ir sak\u0101rtota<\/em>:<\/p>\n

\"\"<\/p>\n

II Saskait\u012b\u0161ana<\/p>\n

\"\"
\n<\/span><\/p>\n

III Reizin\u0101\u0161ana<\/p>\n

\"\"
\n<\/span><\/p>\n

IV – Arhim\u0113da \u012bpa\u0161\u012bba<\/p>\n

\"\"
\n<\/span><\/p>\n

V- nep\u0101rtraukt\u012bba<\/p>\n

\"\"<\/p>\n

2.2. Natur\u0101lu skait\u013cu kopa<\/p>\n

\"\"<\/p>\n

\n\n\n<\/col>\n<\/col>\n<\/col>\n<\/col>\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u012apa\u0161\u012bbas<\/td>\nNatur\u0101li skait\u013ci<\/td>\nVeseli skait\u013ci<\/td>\nRacion\u0101li skait\u013ci<\/td>\n<\/tr>\n
I.1<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
I.2<\/td>\n–<\/td>\n–<\/td>\n+<\/td>\n<\/tr>\n
II.1<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
II.2<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
II.3<\/td>\n– (atkar\u012bgs no def.) Pie Asmus – iek\u0161 datZ +<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
II.4<\/td>\n–<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
II.5<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
At\u0146em\u0161ana<\/td>\n –<\/span><\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
III.1<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
III.2<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
III.3<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
III.4<\/td>\n –<\/span><\/td>\n–<\/td>\n+<\/td>\n<\/tr>\n
III.5<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
III.6<\/td>\n+<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
IV<\/td>\n+ (neierobe\u017eota no aug\u0161as)<\/td>\n+<\/td>\n+<\/td>\n<\/tr>\n
V<\/td>\n+- (tjipa ir sp\u0113k\u0101, bet bez I.2 nav j\u0113gas no t\u0101s)<\/td>\n+<\/td>\n–<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

2.3. Veselu skait\u013cu kopa<\/p>\n

\"\"<\/p>\n

2.4. Racion\u0101lu sk. Kopa<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Alternat\u012bva Q defin\u012bcija<\/p>\n

\"\"<\/p>\n

Iracion\u0101lu skait\u013cu kopa sast\u0101v no bezgal\u012bgiem bezperiodiskiem da\u013cskait\u013ciem<\/p>\n

\n

2.5. Skait\u013cu kopas minim\u0101lais un maksim\u0101lais elements; inf\u012bms un supr\u0113ms<\/p>\n

E – skait\u013cu kopa<\/p>\n

\"\"
\n<\/span><\/p>\n

2.5.1. Skait\u013cu kopas minim\u0101lais un maksim\u0101lais elements.<\/p>\n

\"\"
\n<\/span><\/p>\n

X0<\/sub> = minE<\/p>\n

\"\"
\n<\/span><\/p>\n

X0<\/sub> = maxE<\/p>\n

Funkcijas max un min.<\/p>\n

\"\"
\n<\/span><\/p>\n

2.5.2. Ierobe\u017eotas un neierobe\u017eotas skait\u013cu kopas<\/p>\n

Skait\u013cu kopa E ir ierobe\u017eota no aug\u0161as <=> Eksist\u0113 t\u0101ds M, ka visiem x no E x<= M<\/p>\n

M – kopas E ma\u017eoranta <=> M no R un Visiem x no E x <= M<\/p>\n

M – kopas E ma\u017eoranta => visiem M’ no R M’ > M => M’ – kopas E ma\u017eoranta<\/p>\n

maxE – kopas E ma\u017eoranta<\/p>\n

Skait\u013cu kopa E ir ierobe\u017eota no apak\u0161as<=> Eksist\u0113 t\u0101ds m, ka visiem x no E x>= m<\/p>\n

m – kopas E minoranta <=> m no R un Visiem x no E x >= m<\/p>\n

m – kopas E minoranta => visiem m’ no R m’ < m => m’ – kopas E minoranta<\/p>\n

minE – kopas E minoranta<\/p>\n

Kopa E – ierobe\u017eota <=> (E ierobe\u017eota no apak\u0161as & E ierobe\u017eota no aug\u0161as )<\/p>\n

\"\"
\n<\/span><\/p>\n

Ierob. no aug\u0161as – ma\u017eor\u0113jama<\/p>\n

Ierob. no apak\u0161as – minor\u0113jama<\/p>\n

E – neierobe\u017eota no aug\u0161as <=> Visiem M no R Eksist\u0113 x no E : x>M<\/p>\n

E – neierobe\u017eota no apak\u0161as <=> Visiem m no R Eksist\u0113 x no E : x<M<\/p>\n

E – ir neierobe\u017eota <=> ( E – neierobe\u017eota no aug\u0161as V E – neierobe\u017eota no apak\u0161as )<\/p>\n

\n

2.5.3. Skait\u013cu kopas inf\u012bms un supr\u0113ms<\/p>\n

Piem\u0113ri:<\/p>\n

E = ]0,1[ – !eksist\u0113 minE , !eksist\u0113 maxE<\/p>\n

0 – inf\u012bms == infE<\/p>\n

1 – supr\u0113ms == supE<\/p>\n

E = [0,1] – infE = minE = 0; supE = maxE = 1<\/p>\n

N<\/p>\n

1 = minN = infN<\/p>\n

!Eksist\u0113 maxN, bet supN = +infinity<\/p>\n

\"\"<\/p>\n

Ja eksit\u0113 minE => infE = minE<\/p>\n

Ja eksist\u0113 maxE => supE = maxE<\/p>\n

\n

2.5.4. Skait\u013cu kopas inf\u012bma un supr\u0113ma eksistence<\/p>\n

Katrai netuk\u0161ai skait\u013cu kopai E eksist\u0113 infE un supE<\/p>\n

\"\"<\/p>\n

2.5.5 Skait\u013cu kopas inf\u012bma un supr\u0113ma raksturojums<\/p>\n

Teor.<\/p>\n

E – netuk\u0161a ierobe\u017eota no aug\u0161as skait\u013cu kopa.<\/p>\n

b – skaitlis<\/p>\n

\"\"
\n<\/span><\/p>\n

Teor.<\/p>\n

E – netuk\u0161a ierobe\u017eota no aug\u0161as skait\u013cu kopa.<\/p>\n

a – skaitlis<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

V\u0113lviens ieraksts no s\u0113rijas “lekciju pieraksti” 2.1. Re\u0101lo skait\u013cu \u012bpa\u0161\u012bbas Aksiom\u0101tiska def. \u012apa\u0161\u012bbu grupas I < II + III * IV Arhim\u0113da \u012bpa\u0161. V Nep\u0101rtraukt\u012bbas \u012bpa\u0161\u012bba I R ir sak\u0101rtota: II Saskait\u012b\u0161ana III Reizin\u0101\u0161ana IV – Arhim\u0113da \u012bpa\u0161\u012bba V- nep\u0101rtraukt\u012bba 2.2. Natur\u0101lu skait\u013cu kopa \u012apa\u0161\u012bbas Natur\u0101li skait\u013ci Veseli skait\u013ci Racion\u0101li skait\u013ci I.1 + + + […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/posts\/80"}],"collection":[{"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/comments?post=80"}],"version-history":[{"count":2,"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/posts\/80\/revisions"}],"predecessor-version":[{"id":83,"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/posts\/80\/revisions\/83"}],"wp:attachment":[{"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/media?parent=80"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/categories?post=80"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ramuuns.com\/blog\/wp-json\/wp\/v2\/tags?post=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}