Understanding Subtraction of Reals: Exploring Associativity and Differences

  • Thread starter Kocur
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In summary, the conversation is about the concept of subtraction and whether it is considered a separate operation or just a shorthand for addition with the additive inverse. While it may seem like subtraction is associative when written as addition of the inverse, it is not separate from addition and is not associative on its own. Mathematicians do not consider subtraction to be a distinct operation and instead view it as a shorthand for addition with the additive inverse.
  • #1
Kocur
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Well, you might consider my remark to be really silly :smile:. I was thinking about subtraction of reals and the following ideas came to my mind:

From one side, we may consider subtraction to be addition of the inverse of an element, for example:

(5 - 3) - 2 = (5 + (-3)) + (-2).

This "version" of subtraction is associative and (5 + (-3)) + (-2) = 5 + ((-3) + (-2)).

On the other side, if we treat subtraction separately from the addition, it is not associative:

(5 - 3) - 2 is different from 5 - (3 - 2).

Kocur.
 
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  • #2
Yes,it's actually the "+" operation (called addition) that comes into abstract fields,rings and algebras definition.

As u can check,"+" is an associative operation.

Daniel.
 
  • #3
In general mathematicians do not consider "subtraction" to be a distinct operation- largely because it would not be associative and associative is a very nice property.
Subtraction is simply shorthand for "add the additive inverse" and, of course, addition is associative.
 
  • #4
Hopefully, Kocur, you've understood from the previous replies that your remark wasn't silly at all.
 

1. What is confusing subtraction?

Confusing subtraction refers to mathematical subtraction problems that may appear difficult or unclear to solve due to a lack of understanding of the concept or complex numbers.

2. How can I simplify confusing subtraction problems?

To simplify confusing subtraction problems, you can break down the numbers into smaller, more manageable chunks or use visual aids such as a number line or manipulatives to understand the concept better.

3. What are some common mistakes made when solving confusing subtraction problems?

Some common mistakes made when solving confusing subtraction problems include misreading numbers, forgetting to regroup, and not understanding the order of operations.

4. How can I improve my skills in solving confusing subtraction?

To improve your skills in solving confusing subtraction problems, practice regularly, seek help from a tutor or teacher, and review basic subtraction concepts such as regrouping and borrowing.

5. Are there any strategies for solving confusing subtraction problems?

Yes, there are several strategies for solving confusing subtraction problems, such as using the "counting up" method, breaking down numbers into smaller chunks, or using mental math techniques such as subtracting from the nearest multiple of 10.

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