Set Of Positive Real Numbers N N is possibly a slightly different case and it usually differs from branch of mathematics to branch of mathematics I believe that is usually includes 0 0 but I believe theory of numbers is easier without it It can be easilly extended in such was to have N Z N Z denoting positive integers naturals
Let V be the set of all positive real numbers Determine whether V is a vector space with the operations below x y xy x y x y cx xc c x x c If it is verify each vector space axiom if not state all vector space axioms that fail Edit Turns out I m going to fail the exam based on what you guys are saying Feb 17 2015 nbsp 0183 32 However once you append zero the resulting set is no longer a group for exactly the reason your are suggesting One interesting thing about the positive real numbers mathbb R cdot is that they are isomorphic to the reals with addition mathbb R
Set Of Positive Real Numbers
Set Of Positive Real Numbers
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Feb 4 2022 nbsp 0183 32 Note This last argument relies on the assumption that the negative real numbers are exactly the opposites of the positive real numbers I don t have the knowledge right now to prove this fact I don t have the knowledge right now to prove this fact Jul 19 2015 nbsp 0183 32 It s the set of invertible positive real numbers endgroup user5402 Commented Jul 19 2015 at 14 53
Aug 1 2022 nbsp 0183 32 The set of positive integers is 1 2 3 4 dots The set of nonnegative integers is 0 1 2 3 4 dots For set of real numbers you would need to include many other non integral numbers too to both the above sets but still there is only one difference i e 0 Aug 9 2018 nbsp 0183 32 But the point is you cannot assume anything about B except 1 its elements are all positive real numbers and 2 if you take a finite number of elements from B and add them up then you get a sum less than two
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Sep 27 2017 nbsp 0183 32 To proceed by contradiction assume that B is not countable Choose some b B since B is not countable there must exist a sum of elements call it c such that c gt nb for some n N Simply consider the next n elements that are greater than b their sum is greater than nb Choosing n 2 b This implies c B with c gt 2 Stack Exchange Network Stack Exchange network consists of 183 Q amp A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers
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Set Of Positive Real Numbers - Jul 19 2015 nbsp 0183 32 It s the set of invertible positive real numbers endgroup user5402 Commented Jul 19 2015 at 14 53