Wp/lus/Galileo-a Thudikkalh

Galileo-a Thudikkalh hi chhiarkawpa khawnkhâwm chhiar sèn loh nihphung pakhat sawina a ni.

A awmzia

Nambar hi 1, 2, 3, ... tiin chhiar chho ta ila, a khat tâwkin binkim a lo lang a. Binkim te chu 1, 4, 9, 16, ... te hi a ni:

$1^{2}=1,2^{2}=4,3^{2}=9,4^{2}=16,5^{2}=25,...$

Tichuan binkim lo tam tak a lo awm ta a ni, entirnan: 2 te, 3 te hi binkim lo a ni. Chuvangin chhiarna nambar zawng zawng nge binkim tam? tiin zawt ta ila, chhiarna nambar a tam fe zawk kan ti mai awm e. Mahse Gelileo-a thudikkalh chuan a inzât tiin a chhang a ni.

A inzâtna chhan

Nambar binkim leh nambar zawng zawng (binkim pawh chhiar vekin) a inzâtna chhan chu, a inkawp të tëa rem theih a nih vang a ni. A inkawp të tëin lo rem ta ila:

1↔1, 2↔4, 3↔9, 4↔16

emaw

$1$↔$1^{2}$, $2$↔$2^{2}$, $3$↔$3^{2}$, $4$↔$4^{2}$, $5$↔$5^{2}$,…,

chutiang zëlin.

Tichuan a inkawpkim thlap theih avangin bikim leh chhiarna nambar zawng zawng a lo inzât ta a ni.

Thudik inkalh a nihna chhan

Binkim zawng zawng khawnkhawm hi B lo ni ta se, chhiarna nambar zawng zawng khawnkhawm hi N tiin lo ziak bawk ila. B chu N chhunga awm a ni. (A chhan: binkim tawh phawt chu chhiarna nambar a ni vek). Hei hi kan nei:

$\mathbf {B} ={1,4,16,25,...}$

$\mathbf {N} ={1,2,3,4,5,6,...}$

Chumi awmzia chu B hi N aiin a te zawk fe tihna a ni, a chhan chu, entirnan: 3 hi N chhungah a awm a, mahsé B chhungah a awm ve lo; chutihlaiin B chhunga awm tawh phawt chu N chhungah a awm vek thung. A chhiarkawp kalphunging lo ziak ta ila:

$\mathbf {B} \subset \mathbf {N}$

$\mathbf {B} \neq \mathbf {N}$

Tichuan B chu a të zawk tihna a ni a, mahse a chungah khian B leh N a inzât kan ti bawk si a, hei vang tak hian thudik inkalh a ni.

En bawk la

• Newtona Thudikkalh
• Phir Thudikkalh
• Dawheh Thudikkalh
• Seville Khaw Lumettu

Thulâkna

• English Wikipedia, Galileo's Parodox [[1]]