devotion & mathematics

  OPEN & CLOSED SETS In this session we see open & closed sets with their properties. OPEN SET : -      A non empty set A in the real line R is called an open set , every point in A is an interior point of A.                                                                     Examples:- * (a, b)  is an open set.  * [a, b] is not open since the end points a, b are not interior points. * Every finite set is not open. * The sets N, Z and Q are not open sets. * The set R of all real numbers is open. * The set of complex numbers |z|<1 is open. * The set of complex numbers |z|  ≤1 is not open. * Every neighbourhood is an open set. Properties of open sets:- 1. Every open set is a union of open intervals. 2. Union of two open sets is open. 3. Intersection of two open sets is ...

  TRIANGLE :        Definition 1: "A triangle is a 2-dimensional geometrical shape with three side."   We also have Definition 2 : "A triangle is a geometrical shape with 3 angles that's why  we called it as a triangle ".  In the definition 1 we define triangle without using the term " angle " but we called it as a triangle.  Why?  According to definition 1  a triangle is an intersection of 3 non-parallel lines.  If any two lines are intersected there must be an angle.  So if suppose the sides of a triangle are named as I,II,III, between the pairwise intersection of 3 lines i.e. intersection of lines I & II there is one angle, similarly between II & III and between III & I there are two angles.  Area of a triangle :                The area is the region bounded by the three sides of a triangle.  Area of a triangle is generally given by A(area of the trian...

[For a  video explanation click the link  https://youtu.be/ejuoFUIyQJ0 ] we often use the term ' angle ' in trigonometry, geometry etc. 'Angle' plays an important role in  mathematics. Everybody know angle30,  angle  60,angle 15...etc.   But the definitition of angle is disappear. Now we see what is angle?👇                                  " ANGLE IS THE AMOUNT OF TURN OF A RAY FROM THE                                                            HORIZONTAL   LINE "                                                      The positions of rays at various angles are shown below people also...

For a video explanation, click the link 👉  https://youtu.be/kXOzH8k_klw      we know sin30= 1/2.     what it means ?   🤔        In a right triangle if the sine of  angle  30  = 1/2   means that  "  the length of hypotenuse is always double the length of opposite side ". For Example ,  Suppose lenth of opposite side = 6 cm   then      lenth of its hypotenuse = 12 cm ***       Note :   If any one has any doubts in trigonometry or any mathematic concern topics please ask in the comment section .Also anybody of you want to give me friendly suggestions  post in the comment section. * what is dimension of an object? * 4th dimensional object Hypercube . * what is angle?   Page navigation #sin30 #= #1/2 #what #it #means #?  #maths #mathematics # trigonometry  #iit #jee #mains #eamcet #iit-jee #iitjee maths  #trigono...