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I have never thought so deeply about addition and subtraction. But today I noticed something. When adding or subtracting numbers, we actually apply the rules we use for vectors (for example, the vectors we use in physics). only it were one size, wouldn't all vectors form a set of real numbers? Or in another way, wouldn't it form the endless set of points that we define as a line in geometry?

For example;

$3-(-1)=4$

If we represent the above subtraction with integers with vectors. We define a $1$-unit vector $\overrightarrow{A}$ going from 0 to the left and a $3$-unit vector $\overrightarrow{B}$ going from 0 to the right.Then we multiply vector $\overrightarrow{A}$ by the scalar $-1$ and add it with vector $\overrightarrow{B}$ . As a result, a one-dimensional $4$-unit vector is formed, going to the right from a point 0 that we defined.

In this case, we use vectors to express some concepts that we define as scalar quantities (for example, temperature). As a result of the measurements we made to say that the temperature of the room has decreased, we see that the temperature of 20 degrees has decreased to 10 degrees. This expression can be defined as 20-10=10. We say that the magnitude of temperature is not a vector concept, but when expressing it, we get help from one-dimensional vectors in temperature changes. Is this true?

ProfRob
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1 Answers1

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Good morning, what you're saying is interesting. Of course, real numbers are vectors, belonging to $(\mathbb{R},+,*)$, which is an $\mathbf{R}$-vector space. It's a one-dimensional version of the plane. However, its vector nature is "trivial," as you mentioned. You can see it as vectors along a line, but there, all vectors have the same direction.

Gorga
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