Bijective Correspondences and Countably Infinite Sets
... Important: if a bijective correspondence exists between two finite sets, they have the same cardinality. To emphasise: Two sets have the same cardinality if �and only if) it is possible to match each element of A to an element of B in such a way that every element of each set has exactly one “partner ...
... Important: if a bijective correspondence exists between two finite sets, they have the same cardinality. To emphasise: Two sets have the same cardinality if �and only if) it is possible to match each element of A to an element of B in such a way that every element of each set has exactly one “partner ...
MAT 140 Discrete Mathematics I
... Taught first class 43 years ago, still learning from my students MMT 400 Discussing place value, issue of why 100 = 1 and 10–n =1/10n. Students were very surprised (actually quite shocked) that I couldn’t give them a reason why these notations had to be defined in this way, that the definitions/nota ...
... Taught first class 43 years ago, still learning from my students MMT 400 Discussing place value, issue of why 100 = 1 and 10–n =1/10n. Students were very surprised (actually quite shocked) that I couldn’t give them a reason why these notations had to be defined in this way, that the definitions/nota ...
lecture notes 4
... 8. Let n > 1 be a positive integer. Suppose that 2n chess pieces are placed at distinct squares of an n × n chessboard. Show that four of these pieces determine the vertices of a parallelogram. Outline. Imagine each pair of pieces as determining a vector in the first or fourth quadrant. There are n( ...
... 8. Let n > 1 be a positive integer. Suppose that 2n chess pieces are placed at distinct squares of an n × n chessboard. Show that four of these pieces determine the vertices of a parallelogram. Outline. Imagine each pair of pieces as determining a vector in the first or fourth quadrant. There are n( ...
Self-efficacy theory
... Employees inherently dislike work and must be coerced into performing. Theory Y assumptions are basically positive. Employees can view work as being as natural as rest or play. ...
... Employees inherently dislike work and must be coerced into performing. Theory Y assumptions are basically positive. Employees can view work as being as natural as rest or play. ...
Sets with a Negative Number of Elements
... Informally, we say f is a subset of g (and write f ⊆ g) if one can remove elements one at a time from g (never removing an element that is not a member of g) and thus either acheive f or have removed f . For example, we might start with the hybrid set f = {a, b, c, c|d, e}. We will remove a few of i ...
... Informally, we say f is a subset of g (and write f ⊆ g) if one can remove elements one at a time from g (never removing an element that is not a member of g) and thus either acheive f or have removed f . For example, we might start with the hybrid set f = {a, b, c, c|d, e}. We will remove a few of i ...
Chapter Nine - Queen of the South
... new horizons come into view. Unsolved problems remain an uncompromising challenge to the ever-questioning human mind seeking for rational formalistic solutions in its right-lobed brain for the novel intuitions in contemplation of its left-lobed counterpart or complement. As with some relations with ...
... new horizons come into view. Unsolved problems remain an uncompromising challenge to the ever-questioning human mind seeking for rational formalistic solutions in its right-lobed brain for the novel intuitions in contemplation of its left-lobed counterpart or complement. As with some relations with ...
