Funnysteps > Start from deep points TOP> 2. What are letters in math?

Start from deep points



Japanese Edition of this page


2. What are letters in math?


THAT IS,
temporary forms of various (or every) kinds of matters.

Any letters can change themselves into any numbers and any matters.

If human gave a letter a role as numbers,
that letter gets a nature and character as numbers
and it acts and moves as numbers

Human decide their roles.
So before we must use them
we make clear their given natures and characters
,
such as integers, natural numbers, negative numbers, decimals, and real numbers.
Its range also is one of characters of letters in math.
We usually use x or y,
as it has full range of real numbers,
that is, from infinitesimal to infinite.
For example,
when we call a range of letter as "domain of definition,"
what it means?
"Definition" means "human made rules."
So, "domain of definition" means "human given ream of numbers,
that is, a range of numbers."


For example, we use expressions of number ranges, such as 3<x<5.
That means "x can change into all numbers of more than 3 and less than 5
and x can take a role as those numbers."

Of course, x can also change into only one number.

A letter has some nature and characters.
It turns that
we can express figures with exactly same roles and exactly same characters except for its sizes
by using one letter at once.

When we are in elementary schools,
we get answer, if we get a number, for example 5 dollars,
by solving a story problem.
But in a fact,
this 5 dollars is a change of your shopping
when you bought 5 notes (19 dollars a note) with 100 dollars.
But, 5 dollars have only a meaning of money with a size of 5 dollars.
And we lose another meaning and it original role of change.
That is, We do not find 5 dollars is a price of a note or some other.
If we set x as the number of buying notes
(but, x is a natural number of 0<x≤5),
x take a role of the number of buying notes.
Then a change turns to 100-19x,
we can easily find a origin of that number, a change.
When we figure some by letters,
we do not find that concrete number.
But that formula shows a origin of that number
and we can find its meanings,
that is, from what that number follows.


When we use letters instead of concrete numbers,
both convenient and inconvenient matters for us happened.
Although this case is simple one,
in a real, for we want to operate complex discussions,
it is a big advantage for us to leave origins of numbers
as our thoughts.
And we can pile up many discussions on it.
So it is important for us to clearly write down processes of out thoughts.

But, we will not feel practice sizes of answers
represented by formulas with letters, I afraid.
It is important for us to input practice numbers into those letters to find them.
(This is one of reasons that we draw graphs.)

And more, im math field,
we usually use letters of countries
where big contributors of math progress were born.
(For example, alphabets of English, Greece and Russian)
That is only our customs.
So math does not mind originally,
if we set any (or all) natural numbers as "."
But if we use in your answers,
that letter will be buried in other words in your answers.
So it is not useful for us.
(Upper situation happens in Japanese case.
So we usually use alphabets of English in Japan.)
If unclear cases what are letters of math in your answers,
we can not inform what we really wrote for what we wanted to write
to markers,
and if they can not understand our answers meanings,
they can not mark right or wrong on our answers.
I recommend you to make devices
to distinguish math letters and sentence words in your answers.





Funnysteps > Start from deep points TOP> 2. What are letters in math?
copyright Funnysteps all rights reserved.
inserted by FC2 system