PROBLEM SET 9 (1) There is always a bi

... the vertex in the ultraproduct corresponding to the sequence bn/2c of vertices in the factors. For any fixed k, there are only finitely coordinates in which this vertex is within distance k of a vertex of degree zero. Thus, by the fundamental theorem of ultraproducts, it does not have distance at mo ...

... the vertex in the ultraproduct corresponding to the sequence bn/2c of vertices in the factors. For any fixed k, there are only finitely coordinates in which this vertex is within distance k of a vertex of degree zero. Thus, by the fundamental theorem of ultraproducts, it does not have distance at mo ...

Explanation-of-a-recursive-formula-1

... example above gives the sequence of odd numbers 1, 3, 5, 7, ... . However, if the initial condition was modified to x1 = 2 or Start = 2, the recursive function would give the sequence of even numbers 2, 4, 6, 8, ... . Unlike a recursive formula, an explicit formula stands alone; that is, it has no a ...

... example above gives the sequence of odd numbers 1, 3, 5, 7, ... . However, if the initial condition was modified to x1 = 2 or Start = 2, the recursive function would give the sequence of even numbers 2, 4, 6, 8, ... . Unlike a recursive formula, an explicit formula stands alone; that is, it has no a ...

these two pages

... 6. Even odds. Let E stand for the set of all even natural numbers (so E = {2, 4, 6, 8, . . . }) and O stand for the set of all odd natural numbers (so O = {1, 3, 5, 7, . . . }). Show that the sets E and O have the same cardinality by describing an explicit one-to-one correspondence between the two s ...

... 6. Even odds. Let E stand for the set of all even natural numbers (so E = {2, 4, 6, 8, . . . }) and O stand for the set of all odd natural numbers (so O = {1, 3, 5, 7, . . . }). Show that the sets E and O have the same cardinality by describing an explicit one-to-one correspondence between the two s ...

PDF

... has an irrational hypotenuse. c2 = a2 + b2 , i.e. c2 = 2, c = 2. Thus, must add irrational numbers. The reals are the totality of all finite and infinite decimal numbers. Def. page 8 in Courant. On functions, y = f (x) if f is any law of correspondence whatsoever. Sequences a0 , a1 , a2 , ... are de ...

... has an irrational hypotenuse. c2 = a2 + b2 , i.e. c2 = 2, c = 2. Thus, must add irrational numbers. The reals are the totality of all finite and infinite decimal numbers. Def. page 8 in Courant. On functions, y = f (x) if f is any law of correspondence whatsoever. Sequences a0 , a1 , a2 , ... are de ...

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 ...