Definition of Successor & Processor in Math

Math successor and math processor are two commonly confused terms, despite their meanings being far removed from one another. If you're stuck on a definition for math successor (used in set theory) or math processor (used in computer science), then you need a couple of solid examples of what they mean and what they are used for.
  1. Set Theory

    • The term math successor is used in set theory. Set theory is a branch of mathematics that involves the relationship and nature of sets, or collections of objects. It's technically possible for any item to be collected into a set (for example, stamps or baseball cards). However, the term "set theory" is usually applied to sets that are mathematical in nature (for example, sets of numbers).

    Definition of Successor

    • According to Eric Weisstein, author of "Successor," a math successor is defined as "for any ordinal number, alpha, the successor of alpha is alpha union {alpha}. This means that for any number alpha, the successor for that number is alpha + 1."

    Examples of a Successor

    • For a finite ordinal number like 1, 2 or 3, the successor for that number is the number + 1. So the successor for 1 is 2, the successor for 2 is 3, and the successor for 3 is 4. Set theory contains other types of ordinals, called countably infinite ordinals, like w, w + 1, and w + 2. The successor for w would be w + 1, and the successor for w + 1 would be w + 2.

    Definition of Maths Processor

    • A maths processor is a term used in computer science to describe any computer. The computer is basically a number processor that processes binary code (0s and 1s) in the central processing unit (CPU).

    Examples

    • A maths processor can be any device or program that handles computer code. For example, a mainframe computer is a maths processor, as is a handheld graphing calculator. Maths processors can also be used to refer to specific pieces of software that crunch numbers and draw graphs.

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