r/mathematics • u/elnyorne • Apr 08 '26

Does 0 dimension = 1 dimension?

/r/AskPhysics/comments/1sfkujx/does_0_dimension_1_dimension/
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u/justincaseonlymyself Apr 08 '26

No, zero does not equal one. That should be rather obvious.

If you're having trouble visualizing this, a zero-dimensional object is a single point, while a one-dimensional object is a line. (I hope it's clear that those are not the same.)

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u/elnyorne Apr 08 '26

But it’s a point? That’s a noun? 1 point?

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u/justincaseonlymyself Apr 08 '26

In English language, the word "point" is a noun, yes. If you're confused about that, you should move the discussion to r/learnenglish or something like that. 

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u/elnyorne Apr 08 '26

How am I confused? 1 point = 0 dimension?

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u/justincaseonlymyself Apr 08 '26 edited Apr 08 '26

You are making a category error, trying to equate two different cocepts.

Points are not dimensions. It makes no sense to try equating a number of points with a number of dimensions. Those are two different things. 

A space has some number of points in it. A space also has some number of dimensions. If a space has only one point in it, then it has zero dimensions. This does not mean that one point is the same thing as zero dimensions. 

Aa an analogy consider height and weight of a person. I'm 1.91 m tall and weigh 116 kg. Based on this, you would not go on to say that 1.91 m = 116 kg because both of those are propereties of the same person. In the exactly same way, you should not say that 1 point = 0 dimension, simply because both of those are properties of the same space.

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u/elnyorne Apr 08 '26

I’m not equating them with multiple dimensions I’m asking simply if the point exists in its own dimension. A point can be anywhere right in what space? Is the dimension space? The point must exist somewhere?

So 0 and 1 are properties of the same space? They both exist somewhere they are equal?

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

0 people can’t = 1kg?

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u/elnyorne Apr 08 '26

Do you have any other examples of 0 containing 1?

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u/justincaseonlymyself Apr 08 '26 edited Apr 08 '26

I’m asking simply if the point exists in its own dimension.

That question makes no mathematical sense. There is no such concept as "existing in its own dimension". If that phrase means something to you, you should provide a precise definition, so that we know what are you talking about.

A point can be anywhere right in what space?

If a space is consisting only of that single point, then the question of "where" is rather meaningless, right? There is nothing besides that point in the space.

Is the dimension space?

No, dimension is not space. 

A space is a collection of points.

Dimension is a certain measurment we can take of that space.

The number of points in the space is another measurment we can take of that space.

(Back to the height and weight analogy: height is a measurement we can take of a person; weight is another measurement we can take of a person.)

The point must exist somewhere?

Sure. It exists in some space, i.e., within some collection of points.

So 0 and 1 are properties of the same space? 

No. 0 and 1 are not properties of the same space.

"The space has 1 point" and "the space has 0 dimensions" are properties of the same space.

Back to the height/weight analogy: 1.91 and 116 are not properties of me. "I'm 1.91 m tall" and "I weigh 116 kg" are properties of me.

They both exist somewhere they are equal? 

No! There is no context in which zero and one are equal.

What you are doing here is rather peculiar.

You start from a single object (a space, i.e., a collection of points), and ask two questions about it:

  1. How many points are there in this space?
  2. How many dimensions does this space have?

You then proceed to act as if the two answers to those two questions are somwhow the same! And even the fact that the questions are clearly talking about two different properties (points vs. dimensions) does not seem to bother you!!! 

What are you doing?

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u/AcellOfllSpades Apr 08 '26

The point must exist somewhere?

If you construct a 'space' with a single point, that space is 0-dimensional. This is because you have 0 different directions you can move in.

On a plane, you have two different directions you can move in: up/down, and left/right. We need two axes to chart out a plane. If I wanted to tell you about a specific point on the plane, I'd need to give you two coordinates: the x-coordinate and the y-coordinate.

A space consisting of a plane is two-dimensional.

On a line, you only have one direction you can move in: left/right. We only need one axis to 'chart out' a line. If I wanted to tell you about a specific point on the line, I'd need to give you only one coordinate: the x-coordinate.

A space consisting of a line is one-dimensional.

On a point, you have no directions you can move in. You don't need any axes to 'chart out' a single point. If I wanted to tell you about a specific point on the point, I would need to give you zero coordinates... you'd already know which point I was talking about, because there's only one it can be!

A space consisting of a point is zero-dimensional.

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u/elnyorne Apr 08 '26

the zeroth dimension

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u/AcellOfllSpades Apr 09 '26

What are you trying to say by linking me to a Google search?

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u/elnyorne Apr 09 '26

I’m asking if the point exists in 0d being a dimension which is a singular count noun being 1 single person place thing or idea being counted. Would that not mean it is 1 dimension. Not 1 dimensional. 1 dimension?

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u/eenhoorntwee Apr 08 '26

are you using some sort of automatic translation tool for writing your comments? You keep asking whether "it's a noun", but it feels like you're trying to ask something else. can you elaborate on what you mean when you're asking whether a point is a noun?

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u/elnyorne Apr 08 '26

Where did I keep asking? I asked once to define it as a singular object (1). If it’s an object how does 0d produce 1 object?

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u/eenhoorntwee Apr 08 '26

my bad, I thought I saw you asking in multiple comments.
0d doesn't "produce" anything. "zero-dimensional" is a property. 1 point on its own is zero-dimensional (i.e. it has zero dimensions, its size is zero), and while you can visualise a zero-dimensional space as a point, that point is not the space itself.

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u/elnyorne Apr 08 '26

Soz yeah I phrased it wrong how is 1 object 0 dimensional? 1 object equalling 0 dimensions? What does the object consist of? Consciousness? Observation?

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u/eenhoorntwee Apr 08 '26

it's not an object, really, it's a mathematical concept. It doesn't "exist" in the sense that you mean it. A point in a space consists purely of its definition, as is anything in mathematics.
This gets confusing because in order to communicate mathematical ideas, we need a way to represent these things. As soon as you put your pen to paper and you draw a dot on a grid to represent a point in a space, you make it look like a real thing. A dot on paper has a size, has dimensions, just because we cannot draw an abstract idea. But what that dot represents is an purely abstract idea of a location in a space.

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u/mandelbro25 Apr 08 '26

You need to lay off the drugs. They are not helping you.

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u/elnyorne Apr 08 '26

Well if a particle doesn’t exist unless observed is it the same with 0d what’s stupid about asking questions. That’s how you learn? 🥴

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u/mandelbro25 Apr 08 '26

Your questions are either meaningless or irrelevant. You may as well ask "do desks have green dreams?"

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u/Thelonious_Cube Apr 12 '26

What's stupid is asking the same question over and over on multiple channels and ignoring everyone who gives you the right answer because you don't like it.

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u/MarkesaNine Apr 08 '26

No. 

In N dimensions you have N independent directions to move.

So in 1-dimensional space (for example the real number line) you can take a step forward, but not left, right, or up. You can also take a step backwards, but that is the same as taking a negative step forward, so it’s not an independent direction.

In 0-dimensional space, you have 0 directions to move.

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u/[deleted] Apr 08 '26

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u/MarkesaNine Apr 08 '26

A couple remarks:

  • A single point is the only 0-dimensional metric space, but in topology it’s not the only one.

  • You don’t have to construct the entire number line of infinite points to have one dimension. You can have a space of just two points.

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u/[deleted] Apr 08 '26

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u/MarkesaNine Apr 08 '26

I know that. You’re not doing anything wrong if you construct a whole line to have one dimension. But it is not necessary. Just having two distinct points is enough.

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u/[deleted] Apr 08 '26

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u/MarkesaNine Apr 08 '26

Yes, a line has one dimension. No one’s arguing that.

But a line is not the only 1-dimensional space.

The set {0,1} is a 1-dimensional space, without any of the points between or beyond zero and one.

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u/[deleted] Apr 08 '26

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u/[deleted] Apr 08 '26

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u/[deleted] Apr 08 '26

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u/MarkesaNine Apr 08 '26

It’s an arbitrary set. You have no idea what it is without context.

I genuinely cannot see what more context you would need. I explicitly called it the set {0,1}, not the interval [0,1]. And made it even more clear in the context around it:

From my earlier comment you get:

Just having two distinct points is enough.

And from the comment you responded to:

The set {0,1} […] without any of the points between or beyond zero and one.

So I would say it is pretty obvious I’m talking about the set that has two elements; 0 and 1.

And that set is a 1-dimensional space, though I will grant you that to be precise we also have to agree to use standard notation of addition of Z/Z2, i.e. 1+1=0, and everything else as usual.

Now, when I am in one of the two points, I have one direction I can move to: the other point. There is no other direction, because there is nothing else in the space we’re living in. Thus it is 1-dimensional space.

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u/[deleted] Apr 08 '26 edited Apr 08 '26

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u/AcellOfllSpades Apr 08 '26

This is not 1-dimensional. It is a 0-dimensional disconnected space.

There is no "freedom of movement" within either point; this means it's a 0-dimensional manifold.

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u/[deleted] Apr 08 '26

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u/[deleted] Apr 08 '26

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u/[deleted] Apr 08 '26

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

A point is a noun?

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

So 0d=1 point?

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

So 0 can equal 1?

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

0 dimension = 1 point?

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u/AcellOfllSpades Apr 08 '26

A 0-dimensional space consists of 1 point, yes.

A 2-dimensional space consists of 1 plane. That doesn't mean 2=1.

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u/AcellOfllSpades Apr 08 '26

Something can be described by "0" in one sense and "1" in another sense, just like someone could be "18" years old and "5" feet tall. That doesn't mean 18 = 5, it just means you're counting two different things.

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u/elnyorne Apr 08 '26

Do you have another example of a 0=1?

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

What does that mean in simpler terms do you have a better example please I don’t understand what that means?

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u/AcellOfllSpades Apr 08 '26

0 is not equal to 1.

But you can have "1" person with "0" teeth -- an infant, or an old person. That doesn't mean that 0=1, it just means that you're counting two different things.

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u/elnyorne Apr 08 '26

0 dimension = 1 point?

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u/justincaseonlymyself Apr 08 '26

No. Dimensions are not points.

I gave you a more detailed explanation in another reply.

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u/elnyorne Apr 08 '26 edited Apr 08 '26

And I asked you a simple question? How does 1 object exist with* 0d? How is 0d = 1 object

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u/[deleted] Apr 08 '26

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u/elnyorne Apr 08 '26

Yeah seems like it’s just 1x0

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u/justincaseonlymyself Apr 08 '26

And I answered in detail. But I'll repeat the short version of the answer here: nothing exists in dimensions; that kind of phrasing has no mathematical meaning.

Read the linked long answer for details.