measure theory and probability theory

Significant Figures and Measuring Instruments - Let us consider the following entries in a Students' Journal: (a) Weight of a calorimeter = 42 g (measuring instrument used is spring balance) The smallest reading the spring balance can record is 1g. There are 42 of 1 g units of h..

The number of significant figures depends on the instrument used and accuracy required. It is wrong to record diameter as 2 cm. It means the reading is approximated to the nearest 1 cm. If the exact reading is 2 cm then it should be recorded as 2.0 cm. The significant figures expr..

Introduction - In Mathematics, a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematics. It has proved to be of particular importance in the foundations of relation..

Introduction - We use specific number of digits to denote an exact value of a number for required accuracy. The digits used for such a purpose are called significant figures. Suppose a measurement is recorded as 0.6204 cm. It means that the measurement was made correct to the ne..

Question 1 - Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 (n+m) and (n+m+1) are consecutive integers, one of..

Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..

In any application of the theory of sets, the members of all sets under consideration usually belong to some fixed large set called the universal set. Usually we denote the universal set by the letter..

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