Laskushiru

Laskuširu – širutropos, ka mit aftoo deki tsatainmietta. Ine laskuširu, lasku mononai katainen – pasku miepie fu usoting ka mus samasuru mit joku ruuru.

Mahpravda ine laskuširu

Mahpravda je tsatainmiettatropos per ka joku fras glaubena bli vyerena (zettai pravda, lakinai tšigaumie). Brukena ine joku mahpravda: erpravda (hadžimade vyerena pravda – miettaranja) au razpravda (fras dan mahpravdena, hotia imauen vyerena).

Fal fu laskuširu

(Jam andrfal ka aftoo unating; men na eindžin dekinai širu alfaftoo… Mangestuur širutropos.)

Katailaskuširu

Katailasku nasimpel lasku fu katai: ein, ni, tre…. Katailaskuširu per širu katai ting ytten bruk veltting – mangesimpel antaa tšiisai lasku andrlasku made mit yoobi fpašuun, men mit stuur lasku (ttb 157928) treng hyerne os štift-na-paperi.

Jamlasku (Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb N} )

lasku fu tingkatai ka sejena ine pravdavelt. 1, 2, 3… jamlasku; Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scriptstyle\frac12} jamlaskunai. Miettena ka 0 (nil) auen jamlaskutropos, auenli »uso katai«.

Heellasku (Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb Z} )

jamlasku au kundurlasku fu aftoo. Kundurlasku fu Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} tak lasku Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} , ka Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x + y = 0} . Kakena $-x$, hanena »nut $x$« (< ‘ein utn’) os »lop $x$«.

Tellasku ($\mathbb {Q}$)

al lasku ka heellaskunen tel fu andr heellasku.

Gwirlasku ($\mathbb {R}$)

Figlasku ($\mathbb {C}$)

Pravdalaskuširu

Pravdalasku – lasku fu hurmange pravda (os uso). Ine laskuširuvelt letstevikti Buulpravdalasku, ka har ni kundur fal – pravda ($\top$ os $\mathbb {1}$) au uso ($\bot$ os $\mathbb {0}$).

Klaanilaskuširu

Klaani - ine laskuširu, klaani har mange chigau ting. Deki har sofnai ting, os nil ting (de kaku $\emptyset$). Ttb Jamlasku je klaani mit sofnai lasku, men $A=\{1,2,3,4\}$ je klaani mit mono 4 lasku. Ting ine klaani mus chigau je, sitt $\{1,1\}$ sama $\{1\}$. Klaani mavikti ine laskuširu, grun al laskuširu bruk sore.

Havuralaskuširu

Havura – liik klaani, men har plusmange ruruimpla. Klaani $H$ je havura li har kawarina $(\cdot ):H\times H\to H$, ka suru 4 Havurapravda:

1. Peral $a,b$ ine havura $H$, $a\cdot b$ auen ine $H$
2. Peral $a,b,c$ ine $H$, $a\cdot (b\cdot c)=(a\cdot b)\cdot c$
3. Jam tak $e$ ine $H$, ka peral $a$ ine $H$, $e\cdot a=a\cdot e=a$
4. Peral Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a \in H} , jam Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b \in H} , ka Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a \cdot b = b \cdot a = e} (kakuena Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b = a^{-1}} )

Men ine havura, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a \cdot b} naimus Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b \cdot a} sama. Li afto pravda peral Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} au Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} , de Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H} haissa havurafabel (naeme za Niels Henrik Abel).

ṡirunajun (MidoriVals😤)

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Rightarrow, \rightarrow, \supset}

il... je ka...

A sama B naj ak koske A ak au B naj ak koske A na sama B

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = 2 \Rightarrow x^2} = 4 je ak, au Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 = 4 \Rightarrow x = 2} je na akraat perka x miraje -2

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Leftrightarrow, \leftrightarrow, \equiv}

li au mono li, sama

A ⇔ B mono ak A ak au B ak os A naj ak au B naj ak

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x + y = y + 2 \Leftrightarrow x + 3 = y}

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \neg x, \tilde x, !x}

nai, nilatai

$\neg (\neg A)\Leftrightarrow A$

¬A ak, li au mono li A naj ak

$x\neq y\Leftrightarrow \neg (x=y)$

$\land ,\cdot ,\&$

laskiau

$A\land B$ ak li A ak au B ak os je najak

$n<4\land n>2\Leftrightarrow n=3$ koske n je lasku

$\lor ,+,\|\|$

laskios

$n\geq 4\lor n\leq 2\Leftrightarrow n\neq 3$ koske n je lasku

∴ sitt

Alkami naj sinu

Zeuskami je kami

Zeuskami naj sinu

∵ perka

Zeuskami naj sinu

∵ alkami naj sinu au Zeuskami je kami