Mathematic Definitions and Ideas

In summary, "opposite" in mathematics does not have a strict definition. It can refer to various concepts such as inversion, subtraction, complement, dualism, and others depending on the context. However, terms like "converse", "inverse", and "negation" have well-defined meanings.
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I have never posted before. But, I had a question:

What is the mathematical process of "opposite," using the general definition of the word?
What is opposite in Mathematics?

I argued with my engineering brother and his pal that "inverse" is indeed "opposite" if you use the general concept of "opposite." My brother claims that the idea of opposite in mathematics only means returning to null.

Opposite: 1.) Having a position on the other side. 2.) Diametrically different.

Am I totally wrong? Or is the idea of opposite not very applicable?
 
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  • #2
Query said:
Summary: I have never posted before. But, I had a question:

What is the mathematical process of "opposite," using the general definition of the word?

What is opposite in Mathematics?

I argued with my engineering brother and his pal that "inverse" is indeed "opposite" if you use the general concept of "opposite." My brother claims that the idea of opposite in mathematics only means returning to null.

Opposite: 1.) Having a position on the other side. 2.) Diametrically different.

Am I totally wrong? Or is the idea of opposite not very applicable?

"Opposite" numbers mean numbers that are the negative of each other. Apart from that, I'm not aware of "opposite" having any strict mathematical definition.

Instead, there are terms like "converse", "inverse" and "negation", which are all well-defined.
 
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  • #3
There is no specific opposite in mathematics. Depending on context it can refer to:
  • inversion
  • subtraction
  • complement
  • dualism
  • anti isomorphisms
  • indirect conclusion
  • contraposition
The only occasion I can remember to have actually seen something like ##G^{opp}## was when a binary operation of ##G## has been turned from left to right to right to left. So the list goes on with
  • reflexion
  • conversion
  • the two parts of an equivalence relation or conclusion
 
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  • #4
When talking about a proposition one could say "well, consider the opposite.." i.e consider the negation of said proposition. We don't really have anyone specific instance where we say "opposite" about something. In view of @fresh_42 's examples, I prefer to call all those operations what they are instead of potentially confusing the reader/listener - unnecessary.
 

Related to Mathematic Definitions and Ideas

1. What is the definition of a variable in mathematics?

A variable in mathematics is a symbol that represents a quantity that can vary or change in value. It is usually denoted by a letter, such as x or y, and is used to express relationships and solve equations.

2. What is the difference between a function and an equation?

An equation is a mathematical statement that shows the equality of two expressions, while a function is a relationship between two variables in which each input has a unique output. In other words, an equation is a statement, while a function is a process.

3. What is the Pythagorean Theorem and how is it used?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It is commonly used to find the length of a missing side in a right triangle.

4. What is the difference between a prime number and a composite number?

A prime number is a positive integer that is only divisible by 1 and itself, while a composite number is a positive integer that has more than two factors. In other words, a prime number can only be divided evenly by 1 and itself, while a composite number can be divided evenly by at least one other number.

5. What is the order of operations in mathematics?

The order of operations in mathematics is a set of rules that dictate the order in which operations should be performed in a mathematical expression. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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