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Because numbers such as pi, e and the square root of 2 are not rational.
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∙ 10y ago
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Why integers need an extension?
In the first stage, the set of all integers needs an extension - to the set of rational numbers - to get closure for division (which is the inverse operation to multiplication).
Let K be an extension of the field Q of rational numbers?
OK. I'm agreeable. Sounds reasonable to me. K has my permission.
What rational numbers are real numbers?
All rational numbers are real numbers.
Are rational numbers is an irrational numbers?
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Is the sum of two or more rational numbers is it rational or irrational?
The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.
Why whole numbers require an extension?
as whole numbers does not contain negative numbers, so for denoting ( eg: deapth of the sea,etc )negative things they require an extension.
Why do you need a extenstion of rational numbers?
You need an extension because rational numbers are a tiny subset of all real numbers. There are transcendental numbers such as pi and e which are key to geometry and calculus (respectively), the Golden ratio, as well as all the non-rational roots of rational numbers.
Why integers need extension?
In the first stage, the set of all integers needs an extension - to the set of rational numbers - to get closure for division (which is the inverse operation to multiplication).
Why integers need an extension?
In the first stage, the set of all integers needs an extension - to the set of rational numbers - to get closure for division (which is the inverse operation to multiplication).
Why do integers require an extension?
because all numbers like irrational numbers could not be included in the set of integers
Let K be an extension of the field Q of rational numbers?
OK. I'm agreeable. Sounds reasonable to me. K has my permission.
How many rational numbers are there between two consecutive rational numbers?
There are no consecutive rational numbers. Between any two rational numbers there are an infinity of rational numbers.
Is 3.9 rational or irrational?
If there are no numbers after the 9 it is rational
Are some rational numbers are not real numbers?
No. Rational numbers are numbers that can be written as a fraction. All rational numbers are real.
Are rational numbers whole numbers?
The set of rational numbers includes all whole numbers, so SOME rational numbers will also be whole number. But not all rational numbers are whole numbers. So, as a rule, no, rational numbers are not whole numbers.
Is the difference of rational numbers a rational number?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural numbers are rational.
Is 6.6 irrational or rational?
6.6 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
