Question

I want to know something about precise math notations.

Answer 1

If I want to say that the velocity has to be linear, is there any way to denote this mathematically?

Answer 2

well, in general, is there a way to denote something is linear?

Answer 3

If I want to denote, for example, that y is a linear function of x.
Is there way to do this?
(trying to be clear about what I need)

Answer 4

A straight line is obviously linear. Note that the variable x has the exponent 1:\[y=mx^1+c\]

Answer 5

An equation that contains ONLY first powers of x is linear.

Answer 6

\(\color{#000000 }{ \displaystyle y \in mx+b~\forall \{m,b\}\in \mathbb{R} }\)

Answer 7

would that suffice?

Answer 8

Writing the equations of straight lines (linear functions) involves the use of the FIRST power of x. That x is the variable. The constants m and b are fixed.

In other words, if y=mx+b, x and y are variables and m and b are constants.

Answer 9

yes, m and b are constants of course. (did I write something else?)

Answer 10

"Direct variation" is another example of a linear relationship. If y is directly proportional to x, then we write y = kx, where k is the "proportionally constant."

Answer 11

yes, i know.
just that any y=mx+b is shifter vertically for nonzero b.

I am asking about notations. I know what linear functions are.

Answer 12

I appreciate your curiosiy. I also believe that your question and other input show that you could most likely find answers to this type of questions on the Internet. Sorry, but I need to help another person who has a specific math problem to solve.

Answer 13

Sure, ... I wouldn't force you to stay:)
I have searched the web, but didn't find my query.

Answer 14

Thanks for your input tho

Answer 15

Look up something such as "notation: lilnear functions" or the like.

Answer 16

Perhaps, if I want to say that y is a linear function of x, then

\(\color{#000000 }{ \displaystyle y\propto x }\)
but, that is only for direct variation, not for any vertically shifted linear f

Answer 17

\(\color{#000000 }{ \displaystyle y\in\left\{ mx+b\right\}~\forall~m,b \in \mathbb{R} }\)

this might be precise, but it is a little nasty and definitely too long just to denote that y is linearly related with x.

Answer 18

i guess not ....

Answer 19

closing.