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Is -0.9 a irrational number?
No, -0.9 is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and -0.9 can be written as -9/10. Since it can be represented as a fraction, it falls within the category of rational numbers.
Which set of numbers in which -9 belongs to?
The number -9 belongs to several sets of numbers, including the integers, rational numbers, and real numbers. As an integer, it is a whole number that can be positive, negative, or zero. As a rational number, it can be expressed as a fraction (-9/1), and as a real number, it falls within the continuum of numbers on the number line.
What is the opposite of a rational number?
Within the set of rational numbers, positives and negatives are considered opposite.
Is 6.32 a real number?
Yes, 6.32 is a real number. Real numbers include all rational and irrational numbers, and 6.32 falls within this category because it can be expressed as a terminating decimal.
What set of numbers does negative 7.34 belong?
Negative 7.34 belongs to the set of real numbers, as it is a rational number that can be expressed as a fraction (e.g., -734/100). It is also part of the set of rational numbers because it can be represented as a ratio of two integers. Additionally, it falls within the set of negative numbers.
Are 3 real?
Yes, the number 3 is a real number. Real numbers include all rational and irrational numbers, and since 3 can be expressed as a fraction (3/1), it falls within this category. Therefore, 3 is indeed a real number.
Why singleton set is not open in Q?
In the context of the rational numbers ( \mathbb{Q} ) with the standard topology induced by the real numbers ( \mathbb{R} ), a singleton set ( {q} ) (where ( q ) is a rational number) is not open because for any point ( q ) in ( \mathbb{Q} ), every open interval around ( q ) contains both rational and irrational numbers. Therefore, any interval ( (q - \epsilon, q + \epsilon) ) intersects with points outside the singleton set, meaning it cannot be entirely contained within ( {q} ). Thus, singleton sets do not satisfy the definition of an open set in ( \mathbb{Q} ).
Which is greater the rational numbers or set of integers?
Within a given range, the set of rational numbers is greater. Without a given range, both sets are infinite and a comparison is not very helpful.
Number theory is the queen of mathematics?
This is told by Carl F. Gauss: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." There are different types of numbers: prime numbers, composite numbers, real numbers, rational numbers, irrational numbers and so on. This study of numbers is included within the concept of maths and numbers and it is very important a study. Therefor number theory holds a greater importance too.
How are the real number system related?
The real number system is composed of several subsets, each with distinct characteristics. It includes natural numbers (counting numbers), whole numbers (natural numbers plus zero), integers (whole numbers and their negatives), rational numbers (fractions of integers), and irrational numbers (non-repeating, non-terminating decimals). These subsets are nested within each other, with rational and irrational numbers together forming the complete set of real numbers. This hierarchical structure allows for a comprehensive understanding of numerical relationships and properties.
Which number when 1.divided by 9 gives remainder 8 2.divided by 8 gives remainder 7 3.divided by 7 gives remainder 6 4.divided by 6 gives remainder 5 and so on till it is divided by 2 and remaider 1?
Remove the common factors. 6 = 3 x 2...as 3 is contained within the number 9 and 2 is contained within the number 8 then 6 is discarded. 4 is contained within the number 8 and is discarded 2 is also contained within the number 8 and is discarded. Take the product of the remaining numbers and subtract 1. (9 x 8 x 7 x 5 x 3) - 1 = 2520 -1 = 2519.......is the solution.
What is a rational group?
A rational group is a mathematical concept in group theory that refers to a group whose elements can be expressed in terms of rational numbers or, more generally, in terms of a rational field. Specifically, it often pertains to the study of algebraic groups and their rational points, where the group operations can be defined using rational coefficients. In this context, a group is considered rational if it has a set of generators and relations that can be defined over a rational field, making it possible to analyze its structure within the realm of rational numbers.
