DOC
... Theorem 2. The Second Principle of Mathematical Induction: A set of positive integers that has the property that for every integer k, if it contains all the integers 1 through k then it contains k + 1 and if it contains 1 then it must be the set of all positive integers. More generally, a property c ...
... Theorem 2. The Second Principle of Mathematical Induction: A set of positive integers that has the property that for every integer k, if it contains all the integers 1 through k then it contains k + 1 and if it contains 1 then it must be the set of all positive integers. More generally, a property c ...
6 The Congruent Number Problem FACULTY FEATURE ARTICLE
... triangle with area n: there are rational a, b, c > 0 such that a2 + b2 = c2 and (1/2)ab = n. In Figure 6.1, there are rational right triangles with respective areas 5, 6, and 7, so these three numbers are congruent numbers. This use of the word congruent has nothing to do (directly) with congruences ...
... triangle with area n: there are rational a, b, c > 0 such that a2 + b2 = c2 and (1/2)ab = n. In Figure 6.1, there are rational right triangles with respective areas 5, 6, and 7, so these three numbers are congruent numbers. This use of the word congruent has nothing to do (directly) with congruences ...
MTHM024/MTH714U Group Theory 4 More on group actions
... regular if it is transitive and the point stabiliser H is a normal subgroup of G; such an action is isomorphic to the action of G/H on itself by right multiplication. In particular, since every subgroup of an abelian group is normal, we see that every transitive action of an abelian group is regular ...
... regular if it is transitive and the point stabiliser H is a normal subgroup of G; such an action is isomorphic to the action of G/H on itself by right multiplication. In particular, since every subgroup of an abelian group is normal, we see that every transitive action of an abelian group is regular ...
One Step At A Time - Carnegie Mellon School of Computer Science
... have shaken. Statement: The number of people of odd parity must be even. Zero hands have been shaken at the start of a party, so zero people have odd parity. If 2 people of different parities shake, then they both swap parities and the odd parity count is unchanged. If 2 people of the same parity sh ...
... have shaken. Statement: The number of people of odd parity must be even. Zero hands have been shaken at the start of a party, so zero people have odd parity. If 2 people of different parities shake, then they both swap parities and the odd parity count is unchanged. If 2 people of the same parity sh ...
Miscellany
... The relevance of this to Ramsey’s theorem is shown by the following result, which generalises the “party problem” (which you may have met). This is a very special case of Ramsey’s theorem. For more on this, see Part 1 of the notes. Theorem 9.2 There is a function F with the property that, if the ed ...
... The relevance of this to Ramsey’s theorem is shown by the following result, which generalises the “party problem” (which you may have met). This is a very special case of Ramsey’s theorem. For more on this, see Part 1 of the notes. Theorem 9.2 There is a function F with the property that, if the ed ...
