Describe the set of numbers that are real numbers but cannot be expressed as one and triggered divided by another rational irrational and proper negative
The set of numbers that are real numbers but cannot be expressed as one number divided by another number where the numerator is rational, the denominator is irrational, and the result is a proper negative rational number can be described as follows:
Let's denote this set as R' and consider its elements.
First, note that any number that can be expressed as a quotient where the numerator is rational, the denominator is irrational, and the result is a proper negative rational number is not included in this set. So, R' will not include numbers like -1, -π, -3.14, etc.
However, R' will include numbers that cannot be expressed in this form. These numbers can be any irrational numbers that are positive, zero, or irrational numbers that are not expressible by dividing one rational number by another irrational number to obtain a proper negative rational result. Examples of such numbers include √2, √3, π, e, etc.
To summarize, the set R' consists of all real numbers that cannot be represented as one number divided by another number, where the numerator is rational, the denominator is irrational, and the result is a proper negative rational number.
The set of numbers that are real numbers but cannot be expressed as one number divided by another number can be defined as irrational numbers. Irrational numbers are real numbers that cannot be expressed as a fraction or ratio of two integers. They are non-repeating and non-terminating decimals.
Now, irrational numbers can be divided into two categories: rational irrationals and proper irrationals.
1. Rational Irrationals: These are irrational numbers that can be expressed as an infinite repeating decimal. Examples of rational irrationals include numbers like 0.101001000100001000001... (the decimal expansion of the square root of 2), or 0.123123123123... (a repeating decimal without a clear pattern).
2. Proper Irrationals: These are irrational numbers that cannot be expressed as an infinite repeating decimal. Examples of proper irrationals include popular numbers like pi (π), the square root of 2 (√2), the square root of 3 (√3), the square root of 5 (√5), and so on.
Therefore, the set of numbers you're asking for are proper irrationals. These are real numbers that cannot be expressed as one number divided by another rational irrational and proper negative.