There are three number line in mathematics:
1. Real Number Line.
2. Imaginary Number Line.
3. Circular Number Line.
1 subset 2 subset 3.
Real Number line, Imaginary line, and circular line are One line. If i got your point, i consider that there is One line, unless if you mean dimensions!
Please explain 1 subset of 2 subset of 3. Also each time you have a curve in the plane regular enough to afford an abcissa ( need to brush on differential geometry here!) you
may call it a number line. So that would make an infinity of "number lines".
In basic mathematics, a number line is a picture of a straight line that serves as abstraction for real numbers, denoted by . Every point of a number line is assumed to correspond to a real number, and every real number to a point.[1]
Often the integers are shown as specially-marked points evenly spaced on the line. Although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing forever in each direction, and also numbers not marked that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers. (https://en.wikipedia.org/wiki/Number_line)
The x, y and z axes are each a straight line where one can find quadrants, where more points and more lines of different shapes, can be found.
A line, as I learned it in my basic education, can already be determined by TWO points.
A circle, as I read it from the book of Setek, can already be determined by THREE points.
The answer to this question could be both mathematical and philosophical, depending on one's DEFINITION of a NUMBER LINE.
If all participants to this thread agree to only one definition of what a number line is, we may have only ONE ANSWER.
But if our perceived definitions of what a number line is differ, we will have different answers.
What I would like to discourage here is DOWN VOTING an answer that does not conform with one's opinion of what a number line is.
Take note thar the more answers we get that differ from ours, the more we learn something new.
Every model of set theory has its real numbers. There exist countable
models of set theory. This seems to conflict with the fact that the real numbers
are uncountable. The answer is that the set is countable from the outside, but not
from the inside. The word choice "all" in "all points on the line", "all Cauchy sequences",
"all decimals" is a problem. If one means that there is a finite number of words that
can describe the number, as "the ratio of the circumference to the diameter of a circle",
or the limit of "Sum 1/n!", then the number of identifiable numbers become countable.
Rear Doctor Yadav : Card(Real Number Line) less than or equal of Card( Imaginary Number Line) less than or equal of Card(Circular Number Line).
Dear Doctor Yadav,
If X is any set, then Card (X ) less than of Card (P(X)) less than of Card(P(P(X))) less than of ...
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