Mathematical induction is a method for proving that a statement is true for every natural number , that is, that the infinitely many cases all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step). A proof by induction consists of two cases.
Team building is a collective term for various types of activities used to enhance social relations and define roles within teams, often involving collaborative tasks. It is distinct from team training, which is designed by a combine of business managers, learning and development/OD (Internal or external) and an HR Business Partner (if the role exists) to improve the efficiency, rather than interpersonal relations. Many team-building exercises aim to expose and address interpersonal problems within the group.
Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its correctness is a theorem of ZFC. Let be a property defined for all ordinals . Suppose that whenever is true for all , then is also true. Then transfinite induction tells us that is true for all ordinals. Usually the proof is broken down into three cases: Zero case: Prove that is true. Successor case: Prove that for any successor ordinal , follows from (and, if necessary, for all ).
A team is a group of individuals (human or non-human) working together to achieve their goal. As defined by Professor Leigh Thompson of the Kellogg School of Management, "[a] team is a group of people who are interdependent with respect to information, resources, knowledge and skills and who seek to combine their efforts to achieve a common goal". A group does not necessarily constitute a team. Teams normally have members with complementary skills and generate synergy through a coordinated effort which allows each member to maximize their strengths and minimize their weaknesses.
Motivation is the reason for which humans and other animals initiate, continue, or terminate a behavior at a given time. Motivational states are commonly understood as forces acting within the agent that create a disposition to engage in goal-directed behavior. It is often held that different mental states compete with each other and that only the strongest state determines behavior. This means that we can be motivated to do something without actually doing it. The paradigmatic mental state providing motivation is desire.