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w_attop_nhds_0_of_lt_1:7,tendsto_right_iff:7,tendsto_subseq:7,term:[0,1,2,3,4,5,7],terminolog:5,ters:6,test:4,text:[0,3,5,7],textbook:[0,1,2],th:4,than:[0,1,2,3,4,5,6,7,8],thank:6,thei:[0,1,2,3,4,5,6,7,8],them:[0,1,2,3,4,5,6,7],theme:3,themselv:[0,4,5],theorem:[0,2,4,5,7,8,9,11],theoret:[2,3,7],theori:[0,1,2,3,6,7,8,11],therefor:[1,4,5,7],thereof:0,thi:[0,1,2,3,4,5,6,7,8,9],thing:[0,1,2,3,4,5,6,7],think:[0,1,2,3,4,5,6,7,8],third:[1,2,3,5,7],thorough:0,those:[0,1,2,3,5,6,7,8],though:[2,3,4,5],three:[1,2,4,5,7],through:[0,1,3,4,5,6,7],thu:[1,3,4,5,7],thumb:4,tighter:[1,3],tightli:5,time:[1,4,5,6,7,8,9],timesav:1,tiresom:7,to_addit:6,to_localinvers:8,tofun:[5,6],togeth:[1,2,3,4,5,7],tomuloneclass:6,too:[0,1,3,5,6,7],tool:[0,1,5,6],top:[0,6,7,8],topic:[4,6],topolog:[1,5,6,8,11],topologicalspac:[7,8],toreal:9,total:1,tour:[7,8],trace:6,tradeoff:3,train:[1,6],tran:[2,4,5,6],trans_assoc:5,trans_refl:5,transform:[2,3],transit:[1,2,5,7],translat:[4,6,7],trap:6,treat:[2,3,5,6,7,8],tri:[1,2,4,6],triangl:[1,2,5],trick:[1,2,4,6,8],tricki:[2,3,4,6],trigger:6,tripl:3,trivial:[3,4,7],troubl:[2,3,5],truncat:4,truth:[1,4],tupl:5,turn:[2,3,4,5,6,7,8],tutori:0,twice:[0,1,7],two:[0,1,2,3,4,5,6,7,9],two_l:4,two_le_of_mod_4_eq_3:4,two_mul:1,type:[0,1,2,3,4,5,6,7,8,9],typeclass:6,typic:1,u:[2,3,5,7,9],ubf:2,ubfa:2,ubg:2,ubgb:2,ultim:0,un:3,unbundl:6,unchang:[1,2],uncom:1,uncount:7,uncurri:7,under:[5,6,7],underli:[0,1,5,6],underneath:[1,3],underscor:[1,2,3],understand:[0,2,3,4,5,6,7],understood:[4,7],unfold:[1,2,3,4,5,7],unicod:[1,3,6],unif:6,uniform:[3,7,8],uniformcontinu:7,uniformcontinuous_iff:7,uniformli:8,union:[1,3,4,5,6,8,9],union_def:3,uniqu:[1,2,3,4,5,7],unit:[5,6,7],univ:[3,7,8,9],univ_set:7,univers:[1,3,5,7,11],unknown:6,unless:[1,2,5],unlik:[3,4],unnecessari:3,unpack:[2,3],unpleas:[6,7],unrel:6,unshad:3,unspecifi:6,unsurprisingli:3,until:[1,4,6,7],up:[0,2,3,4,5,6,7],updat:0,upper:[1,2],us:[0,2,3,4,5,6,7,8,9,11],usabl:6,usag:1,user:[0,6],usual:[1,2,3,4,5,7,9],v:[2,3,5,7],val:5,valid:2,valu:[1,2,3,4,5,6,7,8,9],van:0,varepsilon:[2,7],variabl:[1,2,3,4,5,6,7,8,9],variant:[1,2,7],variat:[1,3,4,5,7,8],varieti:7,variou:[2,3,5,6,9],vastli:2,ve:[6,7],vector:[1,3,6,8],verbos:3,veri:[0,2,4,6,7,9],verifi:2,versa:[1,3],version:[0,1,2,3,4,5,6,7,8,9],vertic:[2,5],vi:5,via:7,vice:[1,3],view:[0,5,6,7],visibl:1,vocabulari:3,volum:9,vs:[0,1,2,3,5],w:[1,6],wa:[1,3],wai:[0,1,2,3,4,5,6,7,9],want:[0,1,2,3,4,5,6,7,8,9],wasn:7,we:[0,1,2,3,4,5,6,7,8,9],weak:6,weaker:[1,2],weav:5,web:[0,1,4],weight:5,weightedaverag:5,weird:[6,7],weirder:8,welcom:[0,1],well:[0,1,2,3,4,5,6,7],were:[2,4,5,7],what:[0,1,2,3,4,5,6,7],whatev:[0,2,4],whatsnew:6,when:[0,1,2,3,4,5,6,7,8],whenev:[1,2,4,5],where:[0,1,2,3,4,5,6,7,8,9],wherea:[0,1,2,3,5,7],wherebi:[5,7],whether:[1,2,3,4,6,7],which:[0,1,2,3,4,5,6,7,8,9],who:[0,7],whole:5,whose:[1,2,4,5,6,7,8],why:[0,2,4,6,7],wieser:0,window:[0,1,2,5],winston:0,wise:5,wish:7,within:[1,2,7],without:[1,2,4,5,6,7,8],withtop:8,wlog:3,won:[2,4,6,7],word:[1,2,3,4,5,7],work:[0,1,2,3,4,5,6,7,8],world:0,worri:[1,3,4,5],worth:[1,2,5],would:[1,2,3,4,5,6,7,8],wouldn:6,wrap:[6,7],write:[0,1,2,4,5,6,7,8,9],written:[1,2,3,4,5,6,7,8],wrong:3,wrote:4,x:[0,1,2,3,4,5,6,7,8,9],x_0:7,x_1:[2,3],x_2:[2,3],x_i:7,x_nonneg:5,xa:3,xai:3,xeq:[2,3],xgt:2,xlt:2,xltz:2,xmem:3,xnt:3,xnu:3,xpo:3,xs:[2,3],xstu:3,xsu:3,xt:3,xtu:3,xu:3,xy:[2,5],y:[0,1,2,3,4,5,6,7,8,9],y_nonneg:5,yball:7,yeq:2,yet:[2,3,4,5,6,7],yield:[1,2,3,4,5,7],ylim:7,ylt:2,you:[0,1,2,3,4,5,6,7,8,9],your:[0,1,2,3,5,6,7],yourself:[2,5],ypo:3,z:[0,1,2,5,6,7,8,9],z_nonneg:5,zermelo:2,zero:[2,3,4,5,6,7,8,9],zero_add:[1,4,5,6],zero_def:5,zero_dvd_iff:4,zero_im:5,zero_l:[4,5],zero_lt_on:[2,4],zero_lt_two:5,zero_mul:[1,4,5,6],zero_r:5,zero_smul:6,zf:2,zlty:2,zsmul:6,zulip:[0,4]},titles:["<span class=\"section-number\">1. </span>Introduction","<span class=\"section-number\">2. </span>Basics","<span class=\"section-number\">3. </span>Logic","<span class=\"section-number\">4. </span>Sets and Functions","<span class=\"section-number\">5. </span>Elementary Number Theory","<span class=\"section-number\">6. </span>Structures","<span class=\"section-number\">7. </span>Hierarchies","<span class=\"section-number\">8. </span>Topology","<span class=\"section-number\">9. </span>Differential Calculus","<span class=\"section-number\">10. </span>Integration and Measure Theory","Index","Mathematics in Lean"],titleterms:{"function":[3,7],"schr\u00f6der":3,The:[2,3],about:1,algebra:[1,5],appli:1,asymptot:8,ball:7,basic:[1,6],bernstein:3,build:5,calcul:1,calculu:8,close:7,compact:7,comparison:8,complet:7,conjunct:2,continu:[7,8],converg:[2,7],countabl:7,defin:5,differenti:8,disjunct:2,elementari:[4,8,9],exampl:1,existenti:2,fact:1,filter:7,fundament:7,gaussian:5,get:0,hierarchi:6,ident:1,iff:2,implic:2,index:10,induct:4,infinit:4,integ:5,integr:9,introduct:0,irrat:4,lean:11,lemma:1,linear:8,logic:2,mani:4,map:8,mathemat:11,measur:9,metric:7,more:1,morphism:6,negat:2,norm:8,number:4,object:6,open:7,overview:0,prime:4,prove:1,quantifi:2,recurs:4,root:4,rw:1,separ:7,sequenc:2,set:[3,7],space:[7,8],start:0,structur:[1,5],sub:6,theorem:[1,3],theori:[4,9],topolog:7,uniformli:7,univers:2,us:1}})