Is it true that a space of 1 dimension has as many points as a space of n dimensions, being n any integer ?

Answer 1

Yes.
Both have infinitely many points. A one dimensional space consists of all possible points a (Infinitely long) straight line. In other words a representation of a one dimensional space is the real numbers. (0, 1, 3.5, -7.836583, and every other number with finitely or infinitely many decimals)
It is possible to show this by contructing afunction f(t)=(x,y,z) which for every value of t gives a different combination of x, y and z. If there are infintely many t's there will be infinitely many (x, y, z) points. (The same argument can be used for any dimension.)

Answer 2

I'm not 100% sure, but I'd have to say YES!

Think about it in this manner - a plane has an infinite area, so it would thus have an infinite number of points. A space with "n" dimensions would also have an infinite volume, and thus have an infinite number of points. Maybe there's another way to think about it that would make this statement false, but as far as I can tell it is TRUE.

Answer 3

You are "working" here with abstract definitions... A space with n dimensions is described by some "axioms".
for n=1 you deal with a straight line. By definition this line contains an infinite number of points...

for n=2 you are dealing with a 2D space which has (by the Euclidian geometry for example) some new "axioms" like 2 paralel straight lines are "intersected" at the "infinite" point and so on... In this plane you can define an infinite number of lines each with an infinite number of points... But infinite is defined as an abstract "number" and you cannot "compare" it... There for you have the same number of points (an infinite) on n-dimensional space taking n="whatever number you like"...

There are some other "theory" in mathematics like "little infinits" (for example on a "real number straight line" between numbers 2 and 3 there are an infinite of numbers but yet you can "see" the margins of it) but this is another "story"...

Answer 4

I'm not sure what you are asking. A 1D space has an infinite number of points, as does a 2D or 3D space. But, infinity isn't really a number. One way to look at it is, a 1D space is like an infinitely long line. A 2D space is plane made of of an infinite number of infinitely long lines. A 3D space is made up of an infinite number of infinite 2D planes, and so on.

Answer 5

Vertices is plural of vertex. Vertex has no direction, basically function. you many times in touch about universal (vector). 2-dimensional section have 2 cartesian axes. three-dimensional domicile have 3 cartesian axes. and so on. .

Answer 6

Yes.

Answer 7

yes when x/p+t/11 > 2

Answer 8

Yes. Both have cardinality of the continuum.

Answer 9

yes

Answer 10

try the answer i type in the another q u asked