Recent content by GreenBeret

In the metric space (\mathbb R, d) 1) d(x,y) = |{tan}^{ - 1}(x) - {tan}^{ - 1}(y)| ,where x,y are real numbers . 2) d(x,y) = |{tan}^{ - 1}(x) - {tan}^{ - 1}(y)|, where x,y are real numbers . Show that (\mathbb R, d) w.r.t (1) and (2) are incomplete metric space . Also, what is the...

What do you think ? Could we define a field on \mathbb R^n ?? If so , how ?

that's not true always . example : take a_i=1 , for all i. So , we get \overbrace{1+1+\cdots+1}^K =K \not > K

For 2 :So, we have showed there a field on \mathbb R^n??for me I need more details here ... 3) We know every finite extension of \mathbb R is \mathbb R itself or it's isomorphic to \mathbb C . The field (\mathbb R^n, +,\cdot) is an extension of (\mathbb R,+,\cdot) or not ?? that what I...

Hey Guys ; I need to discuss this problem with you. 1st of all , I'm going to post some posts about some questions with answers . ======================================================================= Q) Could we define a multiplication operation on \mathbb R^3 to have a field on it ...