??????? ???? ?????? ( + ?? ? ) ?? ?????? ??????? ??????? ?????? ????? ??????? (????) ?? ??????? (?????) ?? ?????? , ???????? ? ?????? ? ????? ?? ????? . ?????? ????? ??????? ??????.

???????? [ ????? ??? ???? | ????? ]

?? ?? ????? ??????? ????? ?????? ??????? ??? ? ?????? , ?? ???? ?? ?????? ^[1] . ????? ????? ??????, ????, ????? ??? ?????? ?????? ????? (?????? ???? ????? ?? ????? ????? ??? ????? ?????), ???? ?????? ?????? ????? ?????:

??

??????? ????? ? ?????? , ?? ?? ????? "????" ?? "????" ??????, ???? ????? ?????? ???????.

? ?????? , ?????? ???? ??15 ?????? ??????? P ?? ?? ????? ( p? ) ??M ?? ?? ????? ( m? ) ?????? ????? ??????. ??????? ???? ?????? ???? ??????? ?????? ??????? ?? ???? ???'??? , Summa de arithmetica, geometria, proportioni et proportionalita (???) ????? ???????? ? ????????? ??????? ??????? ? ?????? ?? 1494 . ^[2] ??????? ?? 1489 ?????? ????? ????? ??????? ? ??+ ?? minus ?? mer (???? ??????? ??????? "???"), ??????. ????? ????? , ????? ?? ????? = , ????? ?? ????? ????? ??????? ? ?????? ?? 1557 ????? ??: "???? ??? ?????? ?????? ??????, ??? ?????? ????? + ??????? '???', ????? ????? ? ??????? '????'.”

???? ????? [ ????? ??? ???? | ????? ]

???? ????? (+) ??? ??????? ?????? ????? ?? ?????, ???? ?????? ${\displaystyle 2+3=5}$. ??? ??, ??? ???? ???? ? ??????? ??????? ????? ?? ????? ?? ????? ??? ????? (????? ${\displaystyle +x}$ ??? ?? ${\displaystyle x}$). ????? ?? ???? ??? ????? ???????? ?? ?????, ?????? ???? ?????? ???? ? ???? ????? ?? (???? ${\displaystyle -5}$ ????? ${\displaystyle +5}$).

???? ????? ???? ??????? ??????, ????? ?????? ??????? ??? ??? ????. ? ????? ???????? ????, ???? ?????? ???????? ? ???? ??????? , ????? ????? ???????? ?????. ??? ????, ???? ????? ????? ?????? ??????? ????? ?????. ????, ???? ????? ???? ?????? ?? ?:

• ???? XOR ("?? ?????" ? ?????? ????? ??: ${\displaystyle \oplus }$): ${\displaystyle 1+1=0,\,1+0=1}$
• ?? ???? (?????? ????? ??: ${\displaystyle \lor }$): ${\displaystyle 1+1=1,\,1+0=1}$

????? ????? [ ????? ??? ???? | ????? ]

????? ?????? ?????? ??? ????? ? ???? ??19 ??? ????? ???? ????? ??? ???? (?), ??? ?????? ????? ????? ? ??? . ?????? ?????? ?????? ?????? ????????, ???? ???? ???? ????????. ?????? ???? ??? ???? ????? ????? ????? ?????.

???? ??????? ?????? ????? ???? U+FB29.

???? ?????? [ ????? ??? ???? | ????? ]

• ????? ?????? (?) ???? ????? ??????? ??????? ? ??????? :
  • ???? ??????: ??????? ?????? ?????? ?? ????? ??????, ???? ?????? ${\displaystyle 5-3=2}$. ????? ??? ???? ??????.
  • ???? ???? ?????? ????? ????? ??? ???? ?? ?????, ??????? ??? ?????? ?????? ??? ???? ????? . ??????, ${\displaystyle -5}$ ??? ${\displaystyle 5}$ ?????.
  • ??????? ?????? ????? ?? ??? ????? ?? ????? ?? ?????? ??? ????? (????, ?? ${\displaystyle x=3}$, ?? ${\displaystyle -x=-3}$, ??? ?? ${\displaystyle x=-3}$, ?? ${\displaystyle -x=3}$). ????? ????, ${\displaystyle -(-2)=2}$. ?????? ???? ??? ????? ????? ?? ???? ??.

?? ????? ???????? ?????? "?????" ?????? ????????. ???? ??????? ?????? ???????, ${\displaystyle -5}$ (????) ???? ???? ??? "minus five", ??? ?????? ????? ???? ?????? ?? "negative five" (?????: ??? ?????). ????, ????? "?????" ??? ?????? ??? ?????? ?????? ???? 1950, ?????? ??????? ???? ????????? ???????, ??? ????? "?????" ???? ???? ??? ???????? ????? ?????. ???? ???, ???? ????? ? ????? ????? ??????? ????? ?? ${\displaystyle -x}$ ??"???? ?? ${\displaystyle x}$" ?? " ????? ????? ?? ${\displaystyle x}$", ??? ?????? ?????? ?? ${\displaystyle -x}$ ????? ????? ???? ?????.

????? ??????? [ ????? ??? ???? | ????? ]

????????, ????? ???????? ??? ${\displaystyle x}$ ???? ?? ${\displaystyle a^{+}}$, ??????? ??X ????? ??a ?????, ?????? ???, ??? ${\displaystyle x}$ ???? ?? ${\displaystyle a^{-}}$, ???? ???? ?? X ????? ??a ?????. ??????, ???? ????? ??? ???? ?????? ?? ????? ?? ${\textstyle {\frac {1}{x}}}$ ??? ${\displaystyle x}$ ???? ?? ${\displaystyle 0}$, ?????? ?? ${\textstyle {\frac {1}{x}}\to +\infty }$ ??? ${\displaystyle x}$ ???? ?? ${\displaystyle 0^{+}}$ (????? ??? ${\displaystyle x}$ ??? ???? ????? ??? ???????), ????? ??? ${\displaystyle x}$ ???? ?? ${\displaystyle 0^{-}}$ (????? ??? ${\displaystyle x}$ ??? ???? ????? ???? ???????) ????? ??? ${\displaystyle -\infty }$ (????? ????, ??? ?????? ??????? ).

????? ????? [ ????? ??? ???? | ????? ]

????? ?????? ??????? ???? ???????? ??????, ???? ?????? ??? ?????? ???? ?????? ????? ???????. ????? ???? ?????? ??????? ?????? ?????? ??? ?? ?? ?????? ????? ?? ??? ?????? ??? ??????? "?????" ?? "?????". ?????, ?? ??? ??????? ????? ???? ??????, ???? ???? ?? ??????? ?????? (????? ???? ????? ?? ??????? ??????? ???? ?????), ????? ????? ???? ?? ??? ????? ?? ????? ??????. ????? ????, ?? ??? ??????? ????? ???? ?????, ???? ???? ?? ??????? ??????? ??? ????? ?? ???? ????? ??? ????? ?????? ???.

? ???? ????? ?????, ????? ??????? ???? ????? ???? ?????: "a" + "b" = "ab" .

? ?????? ???????? , ????? ?????? ?? ???? ??+ ??????: ++, ????? ????? ?????? ????? ??? ???, ?? ??? ????? ????? ?????? ?? ???? =.

???? ?????? C ??????? ???? ??????, ??? ????? ???? ????? ?? ????? ?????? ?? ${\displaystyle 1}$; ????? ????, ??? ????? ????? ????? ?? ?????? ?? ${\displaystyle 1}$. ??????, ?????? ++x ?????? "????? ???? ?? X ?? ${\displaystyle 1}$".

???????? ${\displaystyle 0}$ ???? ????? ????? ?????, ??? ??????? ?? ${\displaystyle -0}$ ???? ????? ????? ???? ??? ${\displaystyle +0}$. ?? IEEE 754 (???) ????? ?? ????? ???? , ???? ?? ${\textstyle {\frac {1}{-0}}=-\infty }$ ???? ?? ${\textstyle {\frac {1}{+0}}=+\infty }$ (????? ????, ??? ????? ??? ? ??? ?? ???? (???) ).

??????? ?????? [ ????? ??? ???? | ????? ]

• ? ????? , ???? ?????? ???? ?????? ?????? ??? ??????? ???? ??? ??? ? ?????? .
• ??????? ???? ?? ???? ?????? (??? ??? ???? ?????? ?? ????? ????? ), ???? ????? ????? ?? ??? ??? ????? ????, ????? ???? ?????? ????? ?? ??? ??? ????? ????. ??????, B? (???? "B ?????") ??? ??? ???? ?? B . ??????, ????? ?? ?????? ???? ????? ???? ?? ????? (???? ++B , ??? ???? ??? B ).
• ???? ?? ??????? ???? ?? ??? ???? ???? ?? ????? ??????? ?? ????? ?? ????? ?? ????? Rh . ?????? +A ???? ?? ??? ?? A ????? ???? Rh, ???? ?B ???? ?? ??? ?? B ??? ???? Rh.
• ? ?????? , ????? ??????? ??????? ?? ???? +, ?? ?? ?? ?????? ?? ???? ???????? ?????? ??? ????? ????? ????? ?? ?????? ????.

????? ?????? [ ????? ??? ???? | ????? ]