A real field satisfies the order property for any a and b except....*1 pointa<b or a>b or a=ba c< bc for any number ca+c < b + c for any number ca < b and b< c implies a<c

The order property of a real field is satisfied for any numbers a and b, except when:

1. a < b or a > b or a = b: This is the basic definition of order in a field. If a and b are the same number, then a cannot be less than or greater than b.

2. a c < b c for any number c: This property is not always satisfied in a real field. For example, if a < b and c is a negative number, then a c > b c. This is because multiplying by a negative number reverses the inequality.

3. a + c < b + c for any number c: This property is always satisfied in a real field. Adding the same number to both sides of an inequality does not change the order.

4. a < b and b < c implies a < c: This property is always satisfied in a real field. This is known as the transitive property of inequality. If a is less than b and b is less than c, then a must be less than c.