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20-es5.2b80aeb524b34d2419df.js
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20-es5.2b80aeb524b34d2419df.js
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(window.webpackJsonp=window.webpackJsonp||[]).push([[20],{"4zk1":function l(n,u,t){"use strict";t.r(u);var e=t("8Y7J");var b=function l(){};var a=t("pMnS"),r=t("3ZQ1"),o=t("vKlC");var i=function(){function l(){}var n=l.prototype;n.ngOnInit=function l(){};return l}();var p=e.pb({encapsulation:0,styles:[["h1[_ngcontent-%COMP%]{font-size:2.4rem;font-weight:500;display:inline-block;margin:8px 0}h1[_ngcontent-%COMP%], h2[_ngcontent-%COMP%], h3[_ngcontent-%COMP%], h4[_ngcontent-%COMP%], h5[_ngcontent-%COMP%], h6[_ngcontent-%COMP%]{color:#333}a[_ngcontent-%COMP%], input[_ngcontent-%COMP%], li[_ngcontent-%COMP%], ol[_ngcontent-%COMP%], p[_ngcontent-%COMP%], ul[_ngcontent-%COMP%]{font-size:1.4rem;line-height:2.4rem;letter-spacing:.3px;letter-spacing:.03rem;font-weight:400;color:#444}li[_ngcontent-%COMP%] p[_ngcontent-%COMP%]{margin:0}li[_ngcontent-%COMP%]{padding-bottom:8px}ul[_ngcontent-%COMP%]{list-style-type:square}"]],data:{}});function s(l){return e.Mb(0,[(l()(),e.rb(0,0,null,null,1,"h1",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,["REAL NUMBERS"])),(l()(),e.rb(2,0,null,null,93,"ol",[],null,null,null,null,null)),(l()(),e.rb(3,0,null,null,34,"li",[],null,null,null,null,null)),(l()(),e.rb(4,0,null,null,5,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Equations like "])),(l()(),e.rb(6,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(7,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(-1,0,["x^2-3 = 0"])),(l()(),e.Kb(-1,null,[" have no solution in Rational numbers (Q). 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"])),(l()(),e.rb(20,0,null,null,3,"p",[],null,null,null,null,null)),(l()(),e.rb(21,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(22,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(23,0,["\\sqrt2 , \\sqrt[3]3, \\sqrt"," "])),(l()(),e.rb(24,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" The successive extensions of number system gives, "])),(l()(),e.rb(26,0,null,null,3,"p",[],null,null,null,null,null)),(l()(),e.rb(27,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(28,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(-1,0,["N \\subset Z \\subset Q \\subset R"])),(l()(),e.rb(30,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Here, N is the set natural numbers "])),(l()(),e.rb(32,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Z is the set of integers. "])),(l()(),e.rb(34,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Q is the set of Rational numbers. 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"])),(l()(),e.rb(50,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(51,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(-1,0,["2+\\sqrt 5"])),(l()(),e.rb(53,0,null,null,9,"li",[],null,null,null,null,null)),(l()(),e.rb(54,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" The product of a non - Zero rational number and an "])),(l()(),e.rb(56,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" irrational number is always irrational. "])),(l()(),e.rb(58,0,null,null,4,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Eg. "])),(l()(),e.rb(60,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(61,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(-1,0,["3\\times \\sqrt 5"])),(l()(),e.rb(63,0,null,null,32,"li",[],null,null,null,null,null)),(l()(),e.rb(64,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Functions or mapping : "])),(l()(),e.rb(66,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Consider any two non- empty sets A and B. Let f denote some rule which associates with each element of A. an unique element of B. "])),(l()(),e.rb(68,0,null,null,1,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" We then call \"f' as a mapping or a function from A to B. "])),(l()(),e.rb(70,0,null,null,4,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" It is denoted by "])),(l()(),e.rb(72,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(73,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(-1,0,["f : A \\to B."])),(l()(),e.rb(75,0,null,null,5,"p",[],null,null,null,null,null)),(l()(),e.Kb(-1,null,[" Eg : Let "])),(l()(),e.rb(77,0,null,null,2,"app-math-jax",[],null,null,null,r.b,r.a)),e.qb(78,4308992,null,0,o.a,[],null,null),(l()(),e.Kb(-1,0,["f: N \\to N"])),(l()(),e.Kb(-1,null,[" defined by f(x) = 3x. Where x e N. 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