So make the substitution. How is < defined? Apply the definition both to this case, and to the case you're trying to solve, so that you can see what you need to prove.jaqueh said:i'm still stuck, all i can think of is making the d=-c which i define when c+(-c)=0
jaqueh said:I actually ended up figuring it out, thanks tho!
A pretty simple ordered field is a type of mathematical structure that satisfies certain properties, such as being able to add, subtract, multiply, and divide elements within the field. It is called "ordered" because the elements in the field can be arranged in a specific order, and it is considered "pretty simple" because it follows a straightforward set of rules.
A pretty simple ordered field is a specific type of field that follows additional rules, such as being able to arrange its elements in a specific order. A regular field, on the other hand, may not have this ordering property or may follow different rules altogether.
Some common examples of pretty simple ordered fields include the set of rational numbers, real numbers, and complex numbers. These sets follow the necessary properties and can be arranged in a specific order.
A pretty simple ordered field must have certain properties, including closure under addition, subtraction, multiplication, and division, as well as the existence of an identity element for addition and multiplication, and the existence of inverse elements for addition and multiplication.
Pretty simple ordered fields have various applications in mathematics, such as in algebra, geometry, and analysis. They are also commonly used in economics, physics, and engineering for modeling and solving real-world problems.