Is there a definition of the math object

Quantity (grouping of math objects)

Every scientific subject has its “own” language, for example the element symbols in chemistry. In mathematics there are also a variety of spellings, for example a grouping of values ​​or variables. This grouping is called a set in mathematics. According to the mathematical definition, a set is a collection of mathematical objects (i.e. numbers, letters). The grouped objects belong to the set and are referred to as elements of the set

The set - a collection of mathematical objects

As mentioned at the beginning, a lot is a mathematical object that itself is a summary of mathematical objects. At first glance, grouping values ​​and variables into a set appears to be “banal”. However, a precise description of a “set” is crucial for many (physical) processes. If a set were not clearly defined, a computer processor would never be able to process data, compare groups or the like.

Let's start simply: If an object (let's take the number 5, for example) is part of the set M, this “state of affairs” is described mathematically unambiguously: 5∈ M (=> 5 is an element of M). If the number 5 is not part of the set M, cross out the “∈” at an angle, which means “is not a subset” of. With the help of these two expressions we can uniquely assign any mathematical object to a set or show that the object is not part of the set.

Of course, we also want to compare quantities with one another (e.g. measurement results from experiments). A set can also be a subset of another set. For example, a set M is called a subset of a set N if every element of M is also an element of N (this is expressed mathematically as follows: M ⊆ N or N ⊇ M, “is a subset of”). In mathematics, however, it is often simplified: If A ⊆ B and B ⊆ A, then the sets are both equal and A = B can also be written.

If not all elements of the set M and the set N are equal, then there is the so-called “intersection” and the “union”.

  • Intersection of the set M and the set N: The intersection (of the set M and N) are all elements that are elements of M and N. Mathematically written as: M ∩ N
  • Union of the set M and the set M: The union (of the set M and N) are the elements that are elements of M or of N. Mathematically written as M ∪ N

All elements of sets are summarized by a curly bracket: M = {a, b, c} (this is called an enumerated representation, in higher classes a descriptive representation is often chosen, e.g. A: = {a | a ∈ R) )

example

M = {1, 2, 3} and N = {1, 2, 3, 4]

  • M is a subset of N: M ⊆ N
  • M ∩ N = {1, 2, 3}