Math 140A Homework 2 (Solutions)
نویسنده
چکیده
where the coefficients are real numbers and bm 6= 0. (i) Define addition and multiplication of two elements of F to be the usual addition and multiplication of functions. Show that with this addition and multiplication, F is a field. (ii) We can define an order on F as follows. A rational function like (1.1) is positive if and only if an and bn have the same sign, i.e., anbm > 0. Now given two rational functions p q and f g we define
منابع مشابه
Math 140A Homework 7 (Solutions)
Solution. (a) We will prove the contrapositive. Suppose ⋃i∈I Ai is not connected. Then there exist nonempty separated sets E,F ⊆ X such that ⋃ i∈I Ai = E ∪ F . Since ⋂ i∈I Ai is nonempty, we may pick an x ∈ ⋂ i∈I Ai. Since ⋂i∈I Ai ⊆ ⋃i∈I Ai = E ∪ F , it follows that x ∈ E ∪ F . Without loss of generality, assume x ∈ E. Then x ∈ Ai ∩ E for all i ∈ I. Moreover, F is nonempty, so there exists a y ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017