Aplicación de Los Números Reales

 

Andquc J. Qcsucnvcs prdancibs brjtiêtjhds y bn`carbjhds.

Ck Ibtciâtjhbs, pbrb rcsdnvcr prdancibs , sc kchcsjtb hdkdhcr hjcrtds prdhcgjijcktds quc pcrijtbk nnc`br b nb sdnuhjøk, pcrd bktcs gc nds prdhcgjijcktds cs jipdrtbktc hdkdhcr prjicrd nds köicrds   yb quc nds mby gc gjstjktds tjpds, pucs kd sc rcguhck b nb njstb g c 2, 1, 8, 7, … k, quc sc hdkdhck hdid köicrds kbturbncs. \cbids… 

BN@D GC MJXWDQJB

Kuicrdnd`éb C`jphjb

Köicrds Ibybs Ibybs  

Uucs ajck, tdgds nds köicrds quc sc mbk hdicktbgd sc b`rupbk ck ukb `rbk lbijnjb…  

… NB LBIJNJB QCBN D LBIJNJB GC NDX N DX KSICQDX KSICQDX QCBNCX  quc sc sjktctjzb b hdktjkubhjøk6  KBWSQBNCX . . . . . . . ( K ) KSICQDX CKWCQDX . . . . . . . . . ( V ) QCBNCX ( Q ) QBHJDKBNCX . . . . . . ( R ) JQQBHJDKBNCX . . . . . ( R ·)

 B hdktjkubhjøk, sc pnbktcbk y rcsucnvck cfcrhjhjds y prdancibs gdkgc sc bpnjhbk bn`ukds gc nds köicrds bktcs ickhjdkbgds, pbrb nd hubn cs hdkvckjcktc hdkdhcr nb ncy gc nds sj`kds bsé hdid hjcrtbs rc`nbs gc dpcrbhjøk hdid nbs sj`ujcktcs6

Bn tckcr 1 köicrds gc j`ubn sj`kd, sc suibk y bn rcsuntbgd sc nc bktcpdkc cn sj`kd hdiök gc cnnds. Cfcipnds6

+3 + 1 9 +0

-< -1 9 -= -=  

Kuicrdnd`éb C`jphjb

Köicrds Ibybs

Nb Ibtciâtjhb d nb „Qcjkb gc nbs Hjckhjbs’ , hdid nb nnbiø cn Ibtciâtjhd Bnciâk @buss, cs mdy pdr mdy cn nck`ubfc ukjvcrsbn gc nb hjckhjb, pcrd kd kbhjø gc nb kdhmc b nb ibòbkb? kbhjø gc nb kchcsjgbg gcn mdiarc gc hdktbr y icgjr, cs bsé hdid sur`ck pdr prjicrb vcz nds köicrds, quc ck têrijkds `ckcrbncs sdk rcprcscktbhjdkcs sjiaønjhbs, pdr cfcipnd, gc bn`d quc sc tjckc, quc sc pdscc. Hdid pucgc vcrsc,nds köicrds hdkstjtuyck nb absc gc tdgds nds sjstcibs gc hdktcd y icgjgb ck nb bhtubnjgbg, pdr nd quc sdk nb absc gc nbs Ibtciâtjhbs. Gc ibkcrb quc, tdgds nds köicrds quc mdy sc hdkdhck mbk sur`jgd b nd nbr`d gc nb mjstdrjb hdid ukb mcrrbijcktb pbrb rcsdnvcr prdancibs. Bsé lucrdk bpbrchjckgd pdhd b pdhd nds prjicrds köicrds bktc nb kchcsjgbg gcn mdiarc pdr rc`jstrbr nbs hbaczbs gc `bkbgd quc sc tckébk, nbs bribs, nbs pcrsdkbs gc uk pdanbgd, nds auntds gc `rbkds quc sc jabk bnibhckbkgd, cth.? bsé bpbrchck nds köicrds 2, 1, 8, 7, …k. nds köicrds kbturbncs , quc mdy sc rcprcscktbk hdk K y quc hdid su kdiarc nd gjhc, sur`ck gc ukb kchcsjgbg kbturbn gc nds prjicrds mdiarcs quc pdanbrdk nb tjcrrb. Nuc`d, cstds yb kd lucrdk suljhjcktcs pbrb sbtjslbhcr kucvbs y iâs hdipncfbs kchcsjgbgcs, pdr nd quc sur`jcrdk6 cn hcrd , nds köicrds kc`btjvds hdid pbrtc gc nds cktcrds (V)pbrb rcbnjzbr sustrbhhjdkcs d rcprcscktbr pêrgjgbs. Udstcrjdricktc, sur`jø nb kchcsjgbg gc tdibr pbrtcs gc uk tdgd d gc uk cktcrd gbkgd nu`br b nds köicrds rbhjdk bncs R (quc sc hdkdhck ck nb prjibrjb hdid „qucarbgds’ d ck nb schukgbrjb hdid „lrbhhjdkcs’). 

Bn tckcr 1 köicrds gc sj`kds hdktrbrjds, sc rcstbk y bn rcsuntbgd sc nc bktcpdkc cn sj`kd gcn ibydr.

Wjcipd gcspuês, nb datckhjøk gc rbéhcs, hdkgufd b nds +15 ‘  8 9 + 20 Cfcipnds6 +15 ‘

-23 + 3 9 -25 -25  

köicrds jrrbhjdkbncs R·, quc b`rupb nds köicrds quc kd sdk rbhjdkbncs, cs gchjr, quc kd pucgck cshrjajrsc hdid cn

hdhjcktc gc gds gds cktc cktcrds rds hd hdid6 id6 ∖1, ∖3, ∖0, y cn kuicrd υ, cktrc dtrds.

Bn rcsdnvcr dpcrbhjdkcs hdk pbrêktcsjs, hdrhmctcs d nnbvcs…  Dpcrb prjicrd cn jktcrjdr gc nds pbrêktcsjs mbstb cnjijkbrnds, nuc`d cn jktcrjdr gc hdrhmctcs mbstb cnjijkbrnds, pdstcrjdricktc cn jktcrjdr gc nbs nnbvcs mbstb cnjijkbrnbs, bsé sc sjipnjljhb nb dpcrbhjøk y sc datjckc cn rcsuntbgd.

 

btckhjøk y bkb Ajck, pdk iuhmb btckhjøk bkbnjzb njzb gctckjgbic gctckjgbicktc ktc nds sj` ujcktcs cfcipnds cfcipnds rcsucntds6

J (+=) + (-8) += ‘ 8

JJ JJ   (-25) + (+