A Primer on Mathematical Proof
... numbers may help you discover the proof, but it is not sufficient for the final proof write-up. In contrast, you can disprove a statement by finding a single example where the hypotheses hold but the statement fails. Writing Tip: All said, for complicated proofs, it can be a good pedagogical practic ...
... numbers may help you discover the proof, but it is not sufficient for the final proof write-up. In contrast, you can disprove a statement by finding a single example where the hypotheses hold but the statement fails. Writing Tip: All said, for complicated proofs, it can be a good pedagogical practic ...
dartboard arrangements
... to A if B = iq iq+1 . . . in i1 . . . iq−1 for some q, 1 ≤ q ≤ n (cyclic permutation of A), or B = ir ir−1 . . . i1 in . . . ir+1 for some r, 1 ≤ r ≤ n (reversed cyclic permutation of A). For an actual dartboard, these imply that it does not matter which number is uppermost or whether the board is ...
... to A if B = iq iq+1 . . . in i1 . . . iq−1 for some q, 1 ≤ q ≤ n (cyclic permutation of A), or B = ir ir−1 . . . i1 in . . . ir+1 for some r, 1 ≤ r ≤ n (reversed cyclic permutation of A). For an actual dartboard, these imply that it does not matter which number is uppermost or whether the board is ...
Math 3: Unit 1 – Reasoning and Proof Inductive, Deductive
... If Diego goes shopping, then he will buy a pretzel. If the mall is open, then Angela and Diego will go shopping. If Angela goes shopping, then she will buy pizza. The mall is open ...
... If Diego goes shopping, then he will buy a pretzel. If the mall is open, then Angela and Diego will go shopping. If Angela goes shopping, then she will buy pizza. The mall is open ...
Full text
... Have you ever seen Fibonacci's portrait? This photo Is a close-up of the head of the statue of Leonardo Pisano In Pisa, Italy, taken by Frank Johnson in 1978= Since Fibonacci's statue was difficult to find, here are the directions from the train station in Pisa (about 8 blocks to walk): Cross Piazza ...
... Have you ever seen Fibonacci's portrait? This photo Is a close-up of the head of the statue of Leonardo Pisano In Pisa, Italy, taken by Frank Johnson in 1978= Since Fibonacci's statue was difficult to find, here are the directions from the train station in Pisa (about 8 blocks to walk): Cross Piazza ...
An identity involving counting sums of square and triangular numbers
... and again can verify the two requirements Tj + Tk = r2 + 2Ti and k ≥ 0. In this case, j − k = 2|r|, which is strictly positive (and so j > k as required) and even. The ‘usually’ in the statement concerning overlaps of triangles is there because of the case |r| = i, which gives rise to a figure as sh ...
... and again can verify the two requirements Tj + Tk = r2 + 2Ti and k ≥ 0. In this case, j − k = 2|r|, which is strictly positive (and so j > k as required) and even. The ‘usually’ in the statement concerning overlaps of triangles is there because of the case |r| = i, which gives rise to a figure as sh ...
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... be the largest in the set. Now suppose that any set with cardinality n contains a largest element. Let X be a set with |X| = n + 1. Choose any x ∈ X, and consider the set X − {x}. |X − {x}| = n, and so there is a largest element y ∈ X − {x}. The set X is the disjoint union of X − {x} and {x}. Let z ...
... be the largest in the set. Now suppose that any set with cardinality n contains a largest element. Let X be a set with |X| = n + 1. Choose any x ∈ X, and consider the set X − {x}. |X − {x}| = n, and so there is a largest element y ∈ X − {x}. The set X is the disjoint union of X − {x} and {x}. Let z ...
MATH 60 Section 2.3 Multiplying and Dividing Signed Numbers
... Example 11: Write an expression for the following situations using addition of signed numbers and answer the question. a) You deposited a $30 check. Then you wrote a check for $15. What is your net affect? ...
... Example 11: Write an expression for the following situations using addition of signed numbers and answer the question. a) You deposited a $30 check. Then you wrote a check for $15. What is your net affect? ...
Aalborg Universitet Numerical Investigation of the Primety of Real numbers
... different ck, as r is increasing, so it is not possible to predict P(r) from it. Nonetheless, this seems like a promising area of further research. For instance, the eq. (3) gives an absolute minimum for the value of P(r). The maximum value seems to be equal to one for all values of x, with the exce ...
... different ck, as r is increasing, so it is not possible to predict P(r) from it. Nonetheless, this seems like a promising area of further research. For instance, the eq. (3) gives an absolute minimum for the value of P(r). The maximum value seems to be equal to one for all values of x, with the exce ...
