matematik

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matematiske symboler

\ aritmetik og algebra

Aritmetik og algebra
$$\text{=}$$$$\text{lig med}$$$$a = b$$
$$\neq$$$$\text{forskelig fra}$$$$b \neq c$$
$$\equiv$$$$\text{identisk med}$$$$(x + y)·(x - y)-(x^2 - y^2) \equiv 0$$
$$\gt$$$$\text{større end}$$$$a \gt b$$
$$\lt$$$$\text{mindre end}$$$$a \lt b$$
$$\le$$$$\text{mindre end eller lig med}$$$$a \le b$$
$$\ge$$$$\text{større end eller lig med}$$$$a \ge b$$
$$|$$$$\text{går op i, er divisor i}$$$$3|9$$
$$\nmid$$$$\text{går ikke op i}$$$$5|11$$
$$\equiv$$$$\text{kongruent med (modulo n)}$$$$p \equiv q \text{(mod n) (betyder, at }n \equiv p - q); 17 ≡ 12 \text{ mod } 5$$
$$\text{s}f\text{d}$$$$\text{største fælles divisor (hele tal)}$$$$\text{s}f\text{d}(12,30)=6$$
$$\text{m}f\text{m}$$$$\text{mindste fælles multiplum for (hele tal)}$$$$\text{m}f\text{m}(12,30)=60$$
$$n!$$$$\text{fakultet, "udråbstegn"}$$$$n! = n(n-1)....3 · 2 · 1; 5! = 120$$
$$P_\mathit{n,r}$$$$\text{permutation}$$$$P_\mathit{n,r} = n(n-1)...(n - r + 1)$$
$$K_\mathit{n,r} ;\begin{pmatrix} n\\ r\\ \end{pmatrix}$$$$\text{kombination}$$$$K_\mathit{n,r} = \begin{pmatrix} n\\ r\\ \end{pmatrix} = \frac{n(n-1)...(n - r + 1)}{r· (r-1)...3·2·1}$$
$$\text{[ ], ent}$$$$\text{den hele del af}$$$$\left[7\frac{3}{5}\right]=\text{ent 7}\frac{3}{5}=7$$
$$\text{+}$$$$\text{sum (af tal, udtryk, funktioner), "plus"}$$$$3+8, f+g $$
$$\text{-, } \div$$$$\text{differens, "minus"}$$$$3-8, f-g $$
$$\text{· , x}$$$$\text{produkt, "gange"}$$$$6 · 2, 6 \text{ x } 2 $$
$$\text{: , /}$$$$\text{division (brøk), "divideret"}$$$$6 : 2, 6 / 2 $$
$$x^n$$$$\text{potens (n hel positiv)}$$$$x^n = x · x · ...· x \text{ (n gange)}$$
$$\sqrt[n]{x}$$$$\text{rod (n hel positiv)}$$$$\left(\sqrt[n]{x}\right)^n=x$$
$$x^a$$$$\text{potens (a vilkårlig reel)}$$$$x^\frac{5}{7} = \sqrt[7]{x^5}$$
$$|x|$$$$\text{numerisk (absolut) værdi}$$$$|-2|=2$$
$$\text{[ , ]}$$$$\text{afsluttet interval (lukket interval)}$$$$[4,9] = ❴ \text{ }x | 4 \le x \le 9\text{ } ❵ $$
$$\text{] , ]}$$$$\text{halvåbent interval}$$$$]4,9] = ❴ \text{ }x | 4 \lt x \le 9\text{ } ❵ $$
$$\text{[ , [}$$$$\text{halvåbent interval}$$$$[4,9[ = ❴ \text{ }x | 4 \le x \lt 9\text{ } ❵ $$
$$\text{] , [}$$$$\text{åbent interval}$$$$]4,9[ = ❴ \text{ }x | 4 \lt x \lt 9\text{ } ❵ $$