Page 2 - خصائص الأعداد الحقيقة

:‫ ﻳﻠﺨﺺ ﺍﻟﺠﺪﻭﻝ ﺍﻵﺗﻲ ﺑﻌﺾ ﺧﺼﺎﺋﺺ ﺍﻷﻋﺪﺍﺩ ﺍﻟﺤﻘﻴﻘﻴﺔ‬:á«≤«≤ëdG OGóY’C G ¢üFÉ°üN

≈dEG ∞°VCG á«≤«≤ëdG OGóY’C G ¢üFÉ°üN Ωƒ¡ØªdG ¢üî∏e

Üô°†dG :¿EÉa a, b, c á«≤«≤M OGóYCG …’C á«°UÉîdG
™ªédG á«∏jóÑàdG
a·b=b·a á«©«ªéàdG
a+b=b+a ójÉëªdG ô°üæ©dG
(a · b) · c = a · (b · c) (a + b) + c = a + (b + c) ô«¶ædG

a·1=a=1·a a+0=a=0+a ¥Ó¨f’G

a · _1 = 1 = _1 · a^ a ≠ 0 a + (-a) = 0 = (-a) + a

a a »≤«≤M OóY (a + b)

»≤«≤M OóY (a · b)

a(b + c) = ab + ac , (b + c)a = ba + ca ™jRƒàdG

á«≤«≤ëdG OGóYC’G ¢üFÉ°üN õ««ªJ 2 ∫Éãe

‫ ؟‬5 · (4 · 13) = (5 · 4) · 13 :‫ﻣﺎ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﻤﻮ ﹼﺿﺤﺔ ﻓﻲ‬

.‫ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﺠﻤﻴﻌﻴﺔ ﻓﻲ ﻋﻤﻠﻴﺔ ﺍﻟﻀﺮﺏ‬

.‫ﻭﺗﻨﺺ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﺠﻤﻴﻌﻴﺔ ﻟﻌﻤﻠﻴﺔ ﺍﻟﻀﺮﺏ ﻋﻠﻰ ﺃﻥ ﻧﺎﺗﺞ ﺍﻟﻀﺮﺏ ﻻ ﻳﺘﺄﺛﺮ ﺑﺎﻟﻄﺮﻳﻘﺔ ﺍﻟﺘﻲ ﻳﺘﻢ ﺑﻬﺎ ﺗﺠﻤﻴﻊ ﺍﻟﻌﻮﺍﻣﻞ‬

∂ª¡a øe ≥≤ëJ ✓

‫ ؟‬2(x + 3) = 2x + 6 (2

.‫ ﻭﺍﻟﻨﻈﻴﺮ ﺍﻟﻀﺮﺑﻲ ﻷﻱ ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﻻ ﻳﺴﺎﻭﻱ ﺍﻟﺼﻔﺮ‬،‫ﻳﻤﻜﻨﻚ ﺇﻳﺠﺎﺩ ﺍﻟﻨﻈﻴﺮ ﺍﻟﺠﻤﻌﻲ ﻷﻱ ﻋﺪﺩ‬

_»Hô°†dG ô«¶ædG h »©ªédG ô«¶ædG 3 ∫Éãe á°SGQó∏d äGOÉ°TQEG
»©ªédG ô«¶ædG
- 5 ‫ﻟﻠﻌﺪﺩ‬ ‫ﺍﻟﻀﺮﺑﻲ‬ ‫ﻭﺍﻟﻨﻈﻴﺮ‬ ‫ﺍﻟﺠﻤﻌﻲ‬ ‫ﺍﻟﻨﻈﻴﺮ‬ ‫ﺃﻭﺟﺪ‬ »Hô°†dG ô«¶ædGh
8 »©ªédG ô«¶ædG IQÉ°TEG
IQÉ°TGE ¢ùµY »g Oó©d
_5 ‫ﻫﻮ‬ - _5 ‫ﻟﻠﻌﺪﺩ‬ ‫ﺍﻟﺠﻤﻌﻲ‬ ‫ﺍﻟﻨﻈﻴﺮ‬ ‫ﻓﺈﻥ‬ ،- _5 + _5 = 0 ‫ﺃﻥ‬ ‫ﺑﻤﺎ‬ IQÉ°TEG Éeq GC ,Oó©dG ∂dP
Oó©d »Hô°†dG ô«¶ædG
8 8 8 8 ∂dP IQÉ°TEG É¡JGP »¡a

_8( )( )-‫ﻫﻮ‬ _5 ‫ﻓﺈﻥ‬ ، _5 - _8 = 1 ‫ﻭﺑﻤﺎ ﺃﻥ‬ .Oó©dG
- ‫ﻟﻠﻌﺪﺩ‬ ‫ﺍﻟﻀﺮﺑﻲ‬ ‫ﺍﻟﻨﻈﻴﺮ‬ -
5 8 8 5

2_12 (3B ∂ª¡a øe ≥≤ëJ ✓

1.25 (3A

13 á«≤«≤ëdG OGóY’C G ¢üFÉ°üN 1-1 ¢SQódG