Solutions – §4.2 8. The set of all ordered pairs of real numbers with
... 12. Let V be the set of all positive real numbers; define ⊕ by u ⊕ v = uv and define by c v = v c . Prove that V is a vector space. Let a, b and c be positive real numbers and let s and t be real numbers. If a and b are positive real numbers then a ⊕ b = ab is a positive real number. Thus V is c ...
... 12. Let V be the set of all positive real numbers; define ⊕ by u ⊕ v = uv and define by c v = v c . Prove that V is a vector space. Let a, b and c be positive real numbers and let s and t be real numbers. If a and b are positive real numbers then a ⊕ b = ab is a positive real number. Thus V is c ...
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Countability
... The set of real numbers between 0 and 1 is uncountable Sketch: We will assume that it is countably infinite and then show that this is absurd. Assume we can list all the reals between 0 and 1 in a table as follows ...
... The set of real numbers between 0 and 1 is uncountable Sketch: We will assume that it is countably infinite and then show that this is absurd. Assume we can list all the reals between 0 and 1 in a table as follows ...
Math 475 Big Problems, Batch 2 Big Problem 7: Tulie Number
... This was a little boring, so she tried the following. First she picked some positive number. Then: • (a) She subtracted the whole number part from it. If the result was zero, she stopped. • (b) If it wasn’t zero, she took the reciprocal. The result always had a whole number part so she went back to ...
... This was a little boring, so she tried the following. First she picked some positive number. Then: • (a) She subtracted the whole number part from it. If the result was zero, she stopped. • (b) If it wasn’t zero, she took the reciprocal. The result always had a whole number part so she went back to ...
