teme92 said:Hey shortydeb thanks for the quick reply.
That is what I originally thought but do I not need to get a number n that lies before and after 139/159 but not exactly on it? Its very tedious work if that is the case :/
An ordered field is a mathematical structure consisting of a set of elements, along with two operations (usually addition and multiplication) and a relation called "less than" that satisfies certain axioms. These axioms ensure that the elements of the field can be arranged in a linear order, and that the operations follow the usual rules of arithmetic.
While a regular field has operations of addition and multiplication, an ordered field also has a relation called "less than" that allows for the elements to be arranged in a linear order. This means that in an ordered field, there is a concept of numbers being greater or less than each other, whereas in a regular field, all elements are considered equal.
Some examples of ordered fields include the real numbers, the rational numbers, and the complex numbers. These fields all have a linear order defined by the "less than" relation and follow the axioms for an ordered field.
Ordered fields are used in many areas of scientific research, particularly in fields such as physics, chemistry, and economics. They provide a framework for understanding and analyzing data and making predictions based on the relationships between different elements.
No, an ordered field must have elements that can be represented as numbers. This is because the axioms for an ordered field require the elements to have certain properties that can only be satisfied by numbers. However, these numbers can represent a wide range of quantities, including physical measurements, probabilities, and more.