Irrelevant. Do you mean an irrational number? Now that would be relevant.trambolin said:How about the fact that I can squeeze a real number between any two arbitrary points of Q?
So "the set" is Q. For p to be an interior point of Q, there must exist an interval around p, \(\displaystyle (p-\delta, p+\delta)[/quote] consisting entirely of rational numbers. For p to be an interior point of R\Q, the set of irrational numbers, there must exist an interval [itex](p- \delta, p+ \delta)[/itex]] consisting entirely of irrational numbers. There is NO interval of real numbers consisting entirely of rational number or entirely of irrational numbers.\)omri3012 said:Hallo,
My teacher wrote that:
"The set has no interior points, and neither does its complement, R\Q" where R refers real
numbers and Q is the rationals numbers.
why can't i find an iterior point?
thanks,
Omri
Real numbers are numbers that can be represented on a number line and include both rational and irrational numbers. Rational numbers can be expressed as a fraction, while irrational numbers cannot be expressed as a fraction and have an infinite number of decimal places.
An interior point on the number line would be a point that is not at the beginning or end of the number line, but rather somewhere in between. However, since real numbers are infinite and continuous, there is always a number between any two numbers on the number line, making it impossible to find an exact interior point.
Real numbers are used in a variety of ways in everyday life, such as measuring quantities like length, weight, and time. They are also used in financial transactions, calculations, and in many other areas of mathematics and science.
A rational number can be expressed as a fraction, while an irrational number cannot be expressed as a fraction and has an infinite number of decimal places. Additionally, rational numbers can be written as terminating or repeating decimals, while irrational numbers are non-terminating and non-repeating.
We need both rational and irrational numbers to accurately represent all quantities in the real world. Rational numbers can represent exact values, while irrational numbers can represent values that cannot be expressed as a fraction. Together, they make up the infinite set of real numbers that we use in everyday life and in mathematical and scientific calculations.