UPSC

Solve 24x 100 when x is a Natural Number

Solve 24x 100 when x is a Natural Number: Such problems are common in inequalities. Thus, we have provided, in this article, the solution of Solving 24x less than 100 when x is (i) a Natural Number, and (ii) an Integer. We have also provided answers to some Frequently Asked Questions below.

Solve 24x than 100 when x is a Natural Number and an Integer

(i) Solve 24x 100 when x is a Natural Number

The solution for “Solve 24x 100 when x is a Natural Number” is as follows

Given that:

Since x is a Natural Number:

Hence, the solution set for this problem is {1, 2, 3, 4}

(ii) Solve 24x 100 when x is an Integer

The solution for “Solve 24x 100 when x is an Integer” is as follows

Given that:

Since x is an Integer

Hence, the solution set for this problem is {-∞. . . . . . . .-4, -3, -2, -1, 0, 1, 2, 3, 4}

Frequently Asked Questions (FAQs)

Ques) What is a Natural Number?

Ans) A Natural Number is a naturally occurring number. Natural Number is a set of all positive integers, i.e. all numbers from 1 to ∞. The number 0 is not considered a Natural Number. Upon adding the number 0 to the set of Natural Numbers, it becomes the set of Whole Numbers

A Natural Number is denoted with the alphabet N, and a Whole number is represented by the alphabet W. Hence, both the set of Natural Number and Whole Number can be written as

\[N ∈ {\{1, 2, 3, 4………..∞}\}\]

\[W ∈ {\{0, 1, 2, 3, 4………..∞}\}\]

Ques) What is an Integer?

Ans) An Integer is a set of all positive and negative whole numbers. It is represented by the alphabet Z. The number set of Integer also consists of the number 0. Thus, Integer can be written as

\[Z ∈ {\{-∞……..-4, -3, -2, -1, 0, 1, 2, 3, 4………..∞}\}\]

The lowest group and ring of the natural numbers are formed by the integers. To differentiate them from the algebraic integers, the integers in the theory of algebraic numbers are occasionally designated as rational integers. In essence, (rational) integers are rational numbers that are also algebraic integers.

Ques) What is a Real Number?

Ans) A real number is a number that is used in everyday life to quantify a value. In other words, the points on an indefinitely long line known as the number line, where points belonging to integers are evenly spaced, can be thought of as real numbers.

A Real Number is represented by the Alphabet R. For ensuring the accuracy of theorem proofs involving real numbers, the foregoing informal explanations of real numbers are insufficient. The study of real functions, and real-valued sequences are all based on the awareness that a clearer definition was required and the construction of such a concept, which was a significant development in 19th-century mathematics. Real numbers constitute the only Dedekind-complete ordered field, according to the current axiomatic definition. Other typical conceptions of real numbers include infinite decimal representations, Dedekind cuts, and Cauchy sequences’ equivalence classes (of the rational numbers). These definitions are all equivalent since they all meet the axiomatic definition.

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Gautam Kukreja