速報APP / 教育 / Laws Of Logic

Laws Of Logic

價格:免費

更新日期:2016-12-05

檔案大小:1.7M

目前版本:3.0

版本需求:Android 4.0.3 以上版本

官方網站:http://www.411audio.com

Email:johnmichaelkuczynski@gmail.com

聯絡地址:22 Langdon St. L1 Madison Wisconsin 53703 USA

Laws Of Logic(圖1)-速報App

A one to one function establishes a one to one correspondence between two sets. Other expressions for one to one correspondence are mapping relation transformation, and bijection.

If there is a one to one correspondence between two sets---in other words, if the one set can be transformed into the other---then any given statement about the interrelations of the members of the one set can be interpreted as a statement about the interrelations of the members of the other set.

Laws Of Logic(圖2)-速報App

If there is a one-one correspondence between two sets, then both sets are instances of the same

ordinal number.

Laws Of Logic(圖3)-速報App

81. To count the members of a given class K is to biject the members of K with those of an initial segment of the series of positive numbers. Thus, if K is the smallest class containing the letters A, B, and C, to count the members of K is to biject them with the smallest class containing 1, 2, and 3.

82. A recursive function is one that is defined for each of its own outputs, for example, f(x)=x+1.

Laws Of Logic(圖4)-速報App

83. A recursive definition is one that specifies the membership of a class in terms of a recursive function. More precisely, a recursive definition of a class k is one to the effect that, for some object αand some recursionφ,kisthesmallestclasscontainingαandcontaining φ(x)wheneveritcontainsx.

k is recursively defined ≡DF∃α ∃φ k={x: x=α⋁∃y(φ(y)=x)}

Laws Of Logic(圖5)-速報App

84. A recursive function generates progression. A progression is an infinitely long discrete series that has a first member. A discrete series is one each of whose non-final members has an immediate successor. An example of a progression is the series 1, 2, 3, 4, ......

85. A logic is a recursively defined statement class.

Laws Of Logic(圖6)-速報App

86. An analytic truth is one that holds unconditionally.

87. The expression ‘truth of logic’ is ambiguous. Sometimes, a ‘truth of logic’ is one that belongs to some particular logic, and sometimes a ‘truth of logic’ is a truth describing a condition that any given system of logic must be satisfy.