Can someone please tell me what the word "WHOLE" AND "IRRATIONAL" MEAN IN CALCULUS? THANKS
I'd have thought - unless someone corrects me - that they both have the same meaning as they do in basic arithmetic. By a whole number you mean an integer, and by an irrational number you mean a number that can't be represented as the ratio of two integers. 5 and -5 are whole numbers; 4.5 isn't. 14/32 is a rational number; the square root of two and pi are not.
Certainly! In calculus, the terms "whole" and "irrational" have specific meanings.
1. Whole: In calculus, the term "whole" is not commonly used. However, if you are referring to the term "whole numbers," it represents the set of positive integers (1, 2, 3, ...), including zero (0), without any fractions or decimals. Whole numbers are not used extensively in calculus, as calculus primarily deals with real numbers.
2. Irrational: In calculus, an "irrational number" is a real number that cannot be expressed as a fraction, or the ratio of two integers. They are essentially numbers that cannot be expressed accurately by a terminating or repeating decimal. Famous examples of irrational numbers include π (pi) and √2 (the square root of 2). These numbers have infinitely many non-repeating decimal places. Irrational numbers have important applications in calculus, especially in topics like limits, continuity, and analysis.
To determine whether a number is irrational or not, you typically need to prove it using various methods, such as the proof by contradiction or by showing that a number cannot be expressed as the ratio of two integers. Calculus textbooks and online resources often provide exercises and examples to practice identifying irrational numbers.
Hope this helps clarify the meanings of "whole" and "irrational" in the context of calculus!