Sets And Number Systems, Study notes of Mathematics

Lecture notes on sts and number systems

Typology: Study notes

2023/2024

Available from 03/05/2026

adedotun-olawale
adedotun-olawale 🇳🇬

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APTIST: STUDENT FELIS Lop eer BY ABI MPSOEA: aa ne NERSELS Done bef eae, QNib Company Cary upl: gor" Tse se Chidca eer Your priiredy. Lf Pers ae assign ye ores, 16 gow Acad emie ten = Sf COM PL EX NUMBER ANALSIS aver “Zexely Zils a. funetton oF aL and: 6 ey bef | is tke Imeggia cory perk. xk the real port: note l= ST er ES Comp lose Functor Con: be. seprese D8 on’. tires Mee Ferm; Key are. or ara FSP hin Dole ae Weer Eten or. tectecglane | Sree OR Reseron uber. ah eee wed E..: . Hews Fisas) fata Lessee : Y= rene ‘ay Om } “ay = ts) Fees) Pe eee eee Laces ot hy = er bteme) reall Cas “Osmo =I : Pe actly chide 124 @D.. yO, : ‘aad bracket : Can. be. Used: va Tht . bea fivietson, of: Greesian’ Ae 1 y iste: anol. a e Ues | ia Seen : : © les in. Had ee ‘Ushaje. S Is’ Cobad ie : rogs lle) metal Zz me re ps lato oa, een [Tras ; tho. bet Pome lier” 1 0 Has. Firten Pasi Porin’ View ~ Verte A We yo 1s ote i asd. Ss See OSB E90. on : : ae Y ENR Gnd 2. “Is Ne 8 IP y Is —Ve eunol St Ip AL. jand © Lies in Pee 7 fauede ents “8 Ramon Blecé. teh Scanned with CamScanner Reet, SS) BO ang St “3 Ean =3€0° - [20% = eg =x - 1S = 150% =S0 21 Bp bua Pret Queene Lolo/2olf Ne. Te pulas form OF th Complete | rtimber | L 1s Oe. Eeinze) SEs Comm = C: Sw TZ) 8 Cie os Bo = Da. Cosa. “be (Sin I) Dalen 98) - el ang. ‘@rb ce = Sse 44 po |B: oF re “cad. 2s =r eit “1sinp) = te a gaget Lag) : newer? is! C . (2) ne |4 The maclulus and arg by thr Complore Numbe Je Cli) are A) any TE fy 1) and “la Qaand a etek be 2 = BCHO) open Hhs- bracket 22> htlhe recall Bett iy by Comparison %=Ta A=Ta, y= = fa t re fac a yaaa= iy ane = > Bhp, Og eon She Gates! Bly ate) = 45° Saw 4 Is Aa. Cenol oo Fs HV o° Yes 1 in |eo firsts peed cant |= 4s? = GR = : aa Teo : “a 48 Paz © = A/a |: Posacer Is ol Nole- | Its Ln poloe form Is ve On Coos + sina’) pa Coss - — Loox) | OS Coe Hea x). A) 2.C- col + ise u) e) BC+ -CsE 4 Using) | Scanned with CamScanner E NEASES, dé uwuld Le oa Plsaster clear Fellaw Nig Tan IP you. Coma: 1? Gmpus andyal a oe your Nisisa and Gras * ‘ BULER on Exponential RRM aes ole Sis principal argumonct, as re /Z| = Jer = modulus OF perl C9) Sotvep Pash Question ‘noje {201 No II The & sepatid form AB-2L Noa ™ @am & ales he 92h a7 owe Na poltle | oe 2ur-2L : oS P41 = Ro TS Oe Spar! C8) - ety) o tea f= =e = Since. yg Is “ave! and De Dist quadrant H)2nd quadrant acd quadrant ist and. Bra pu adcant © S Lutton Zot 2a Ze .Ftly x= Vy 4S =-l : Sua Lofh a and y eu ~Ve Hien jb ts» Third gpeeskeank Ansurtr Is C : tle papuieiry OF Cot plex, NuNBER ADPITlon. Gf CompLe ALUM BE 2 IF Za xj tly, and ZF tly 4 Ha = (rte) + 1 Cyt) IZ4Z] = = Je taytyty J modulus Oe tan” te) he & is fhe Prin pal rl arguments OF : 2, 42a, petetwe. cS. jes? in” Foch jal (GYBARACCTION (oe Comple% ate Goa ales Say that” Sse = re, ee a ee rele = =ape - © Retnwrer isfA =i me toy oo ‘Admeee 42-23. = @re)iicy, J) 4-2. = @&: -2)48.) Al =|2e-Zi] re Bante The L Lis. Iq Scanned with CamScanner “YERSE4! What shall w we) a + Ly, Mis y profit ged for hidting tat ea = Atle xis we ~ maderiol « enowyfh oF code) Dat aye iy; t ee SEingy > Help offers aad God wi on cm 2 help yeu a e = May , iG 4 1\5) MumPLicailon oF CompLe% Te Oh ) [Nemeer| 4. = et aA id ark ¢ ixt= Pe -) In Cancly ae °. a, Zea. = Da +0y stilts, : Zz ype a ties +25 ; FFL = Dye. — y, ably pod) Z . z= tye JF 2, =z Ken. . : ., : » Foryulor Adore we ae = ap-peloany ied ie “ fle Pron a ' Can cle clue to ia) ie B= Ye FL 2%I, I : |) zee oy O2%= pos, Diviston) of ComPtex — Daz * rie (Numer, gavep pat Ques tle 5; 2 ; aeie/rof NS | Zz _ 2 aaa (S)Hha Compa Be number ne Speen ear ae whe a Lo she firm actly 1s Remember the. Hreory ef JD +L/>. @l-t Qt be i rettenaliging the, Asanminstor Qi-1. a fF Suc quuisien.. by Using 8 ie Simpe icity OF , ConTu quer Funtcrion, Zs at ty ‘ken the - capil of Z uorctien. 45 B=n-Ly pote? oy. Con q System or Fun ction just Change fhe middle Sign ta. Scanned with CamScanner ‘WeR9€ 55 Sacrabe Said bE now Vay self . but i ull Say be thyself+ tag ei abte) 21 he rr Escample ¢ le Z, = [atl and Ze = lel Evaluat® Zz. IA 2o 4 ® > Buee oF Spat Ze oc4tty = ete bes tan Zar Ceose +is ne) ~ pete i fom24. = Ce AR = Igy ne ty = a Ms ie ea ae Scanned with CamScanner r ove thot, Ni ONt Ap Petia h= }s° This CASE.24 tosteots je. JIZPR Qo a “4 Sow Tien : Yee _ = ys a= . => SIRS 2 ot iy Wom = Y and ota a Zo mo ty fron otdotar IZ = tatty. ton Yh gt a aren lal"= pad Lbs oo Set =]. Sm = ye “Ss 272 “og +4" op. 148 2 = Ja (ose + lst 4 ues ; 4 ae a2 za jprruce ~ PRePERTIES OF Mopurus |. : AND PRIN Corre. ARGUMENT — ; e- _ Theck . . : : ZZ, = 4, Zs . SovuT lon | | Gye = ty 22413. Splut IN Z,Z,, = (4 +iy ) C.F bYD AZ, = oat bay B+rtey FY ZZ = 6 mY tia, #53) [2 2Gacwy-iCaytay Z, Zz = (& ~t4)) (og- Z. LY2) 2G, - bray ioeay + Ey, Z= ed] Gcurxy) Tha ee Ss 22, = V Zee tu ‘ Preved Scanned with CamScanner i fer) fe tof | Given curing beter tat ape) ae, ae? eed. gy Lass eech © he ye) arg Z HO, aqgZc On _ =—1nG@) eacraerael ZHZ=2Re (2) =2 pes va Bae Or Nn PE = Lada (De iarn(g) AG = brgZ~ by Zug : Sees Byaaeue we “= 6, —- By oo Sel fr ZF py PERT OF Conair ton |Z 42H =o VD Sum Ge Gn Seti lon OPer Seppe trspat | tomy ageing ie aE T Ruy a ae : Z2qZ ood ZtZ, : 7 Zz t+Z o:- 1] Inlecg® °F Complex number | (zd YSegual to-lmver te. ep | (Fay = en Conggade — 24h yp ee E= ~& Tas bth Soa ee " Zz -7, Scanned with CamScanner i VERSET? N ctrorly. 15 sare. N-36-SA=0 he ; ; Unless he/she 1s. Saved: RS ne —SA—36 = rae ere Salvation is free Fit MSA =" G ; CE Ged: Atl you have -t2 do is-tofa “DA HH) =O CIB. Confess Alt your sins and AccerT A= J or ot x= Tr ae é TESys CHeIsT AS Your. LOP CHeIST AS Tourn. LORD ee ae L= iy or ey } { AnD Personen SANOUR |! ond: ce 45 : wshan. az=tlo yet é SOLves Exampze S-ti2- CoLUTION et Je-in = oly Square bet Side S-Li2 =(2si yy” or [aay = 5-L12 = y+ Lory = 5-12 “eyivtina, He Cormaspredy i sO On olay =- L 12 ke S43 or tl ca , when ats Ji =, (AB fa = +6 ils te = = 5 “News Ron ts a3 S42 Jets = = J5-ila = S- ua =3- eon “4 Se ee > x - yas petite: WH 36 =F Zz ae j44t ow a esas mut vty A = 5 Z= “dd z maltiply Harta A | 2-2 = Hite) = Het tle Scanned with CamScanner | verse 3: Fg Jesus ‘cHkist 1g LORD and _ you Lelie that G “tm -FRom DEATH, you will Le Saved! ANALYSIS CF POLAR FUNCTION lezic 7 Cee, + lSme) Z,=h Cose, +l S182) It Semysly neans Z = Tes ©, + i nsinG), 4 = Tn GsQ th ons, ZZ= Gems tne x 4Z= ieeeene. + L hry es, St Lim so8 os@5. -b iv in YT _Sin®, SO >. Zin = ta oO css Ob L Cy r5c8 aoss-rcertat) parare SinB SO Digs ee (cos a, cos9,- 50, sind) +165 Ces0 sn B,150O,C 6s) . Ke Crt Sn(ete) = SinB, Cos 8, + Sao, Css)) (9 +9) — Cast Cor, - SrBeen®, Ce8Q)-EL) = Co88 C50, Sn, Sn >» ou “Confess Hat OD RaiseD OnE Fo ramereark,, oa Z, 2 lense t Lene) a Zy = “Teemibnalflattta\ Za —_ G8, +isinfy). (care se) 28 C8, Cost, $sin8; sna.” | + Ging 0, = to He) Cos. 08 ‘ev Ea ZL or cwle, 0) + ise 62) 7 ZG. TSS Ay eo : | - Cf, “8 He @- 6). = 1ca®, bcos ZAC o pg 4 Lense, ae Z,-Z,. = 2 eos ese. : 4 U(Geab) = sun.) i “epty eD Bunmpte " : Convert jn 2-60 eo, “7 i Bhsg rectangube # fom “ ; Setuilen - os = Ja @ = =60"" Zaz ae ine) a ei Scanned with CamScanner 5 ; B= ‘12. [cos (68) + isu (¢o?)) Ze LL Ztss(n€) © Was jam, _ L Bx Io. : . Sub} ak £9) ww) from @ ae ~ TN Pps LIUSINOP) prow ge. 6. Leg Gb) Lol ese = Zr = Z+E 22% od sie a De- NIOUVRE 2s. THE OCR EM . yp skates Irek oF gud= = Hy gis 25 8O ae = (ese tisn® ) EZ ope n= 8 == 0's net [sin n8) 4 % bh — ZL wl n€QrZ | ies = 8 AF Zz fue be expressed as what 7 ote A 4.5 ; er . SoLuTLoy Examete > iF Ze cos Lane BOL By _ Pros thet Zz P a) Bes ess he) 2" 4) ~(B1 ‘ BD Zhe a’ ‘Lasm@e)e | B * ) Blocks SS ie (pt? Sin4e -Lasinee pee i va — : Sta C89 40 ~ Sin 30) “Zs C8 O4 eng | | Recme 2 [e586 tise (y ‘Sin A - Stn Bs2510 af conn a by do Mmaounr-e's analy sis Sin 49 - Sin $B : 2 = sR = - 29) caste +80 ; C6)t | S06) 3D = 2. sia (4-28) fet#e) 2 Jeo - © cas IZ dee 6+ i sng]? > i - 2. sen E48) = eal eee A -18) +1 Sinend) < Asin 28 Cs GE a =. Coe) — TsO oe ‘3 _ —F4.L =-LA sin 28 Gs si aAOnd® gee ionastste Scanned with CamScanner [@ctar! Sgn dete | te peed ‘ -4J3 4 or HR as oy YO Be dead = =a |Or eT abe et 2= g | pre's Iso° = = ow ia! cs aust sre singed 220] =-N Bint Yom Nts ond = ze. 1 [culoiia¥e) Honlova¥e)] pe = EAC csr + i stan) 3 iC 5 3 8 = g 1.(9 = IF Ze pfGnerie) Ke : ; Wj) = s-l rae ee Megring) | long tn aoe _ ushen k=20 1 “ 8 (cos sx = +1su xe) zaay' Loso + sino] . sy =I = [ye Ze 3 Cn \ iene Soe os aes Ee VCs ze +isin =) rz, py bce rash + Lom i2@) er oe he. when koa 2 (22 "8 (eos yas + L sen 2b) : BS 3 Scanned with CamScanner Nerselot Lt is not oF him that wills nether OF him thst uns loud F God that Showeth Mercy!!! Nay God have mercy.on Us - To_CRoss - CHECK vt ASHER, | 284 7/247) . AEC Epc: SOLVED pass Question || 25018 No 23 Ze [eas (ore is es Sin ik” n= =o. Sie Zao to n~fi! ie lon ‘Ent mt ‘at ae k=O: ‘edge eH, “Lg! "[easOLOO-F i Sle a te 724 Te [co.8. S +6 eo] \ Za =a [ees oe. i sige) The Seuare, root of C22) % is oda Elie Rn aha Nqgor"s, Fe oh ie fe Oy, | : : Dagar adden” ake | When KE} " Files C se) tsa 5) : I 3% Cae Atisi en 15 Scanned with CamScanner Verselti NO one 1s righ teous, No not one put CHRIST Is Otbr righbeousess: RELATION Given ture non- empty Rant B In-which églement OF Beare. gna to tlomiaevt & : : mamma “nat Releded ts EXAMPLE Q® t= 12,34 G75. Bal, 2322-10} lod 2 be |ke Cor Clorrank oF A and: Ay. = nen ard ye -! Nis reboted boy Whersrber IS prem ANizer op y TDR Dat ble ditwad a8 ope. ; YER HF me Is a relockny; : yee Pe Co ~prembes - SOLUTION 11) fe His Saul -bo" ays qs prime iu lisa. Yo AG When ox perfectly isis of oF Prima. number GR 2, 3, 57 le xen and gee Do RY> "2 » QRA ake 2R8 alo feud is counge bade nek. Co'- Racker cunt : [iets rok 4 ce ee a prem Poembeer be Prune newer ber Scanned with CamScanner Sf thes sutentinn Re |G2G634 - [" nameerar® 1535795 2.2) (8 #) (55) } oo ic éA ond 9 SB then on (21) (2,2) (2,3) (2,4) DES bee , |G0G2 G9, GP3 ra 283, 285, 28) MFT IDSC oC 3 (2 C3) Ry aR2, SRY BRS , Be 384 3AN C42) (3,3) (42) (yD ¥ e, “SR2, Rs, cua, BRE 7 —_ ae an a f Soiu7 ley SRT FRE, PM ce end y nase yet TR, Tea Rey TRS [noes owl J akc Tee 429 TRIO Prema Wl Se esx prins 4 CD) je nse print umeer ry ae wet wth, Hee trun . RY net gaz TFs . aed -. BR2 BRS ~ ape en oe] pe Ca) eR cs 63,9 fas @D GD, ARO" | Cy /&33) Cle ERD het _ _ hptguer 196) ck he 12,3) and be lios eye aUGS,% 10} ond clofinad Ried a ralstion defined lq Relation on Arad & by 5 thy, For HEM, YER, IF [Cx JER I ond Only IE [c2.9;€2,9,60,8D ye Oe Om DI go: Cae CotuTion {C2, 2 2, Ca. 3) (3) Scanned with CamScanner