Could you give examples of things that have a limit and do not occupy a space — Daniel

My patience.

Ha! My exact answer. But then I thought to include my limitless love for my fellow man.

Or if you mean material things, that which makes a thing itself is the limitation that it is not at the same time something else. It would seem, then, that limits are intrinsic.

If James Riley's patience is different from tim wood's patience and neither occupies a space, how do you distinguish James Riley's patience from tim wood's patience?

If James Riley's patience is different from tim wood's patience and neither occupies a space, how do you distinguish James Riley's patience from tim wood's patience? — Daniel

One runs out quicker than the other. You just have to wait and see.

see what?

How are you able to tell someone's patience runs out quicker than someone else's?

How are you able to tell someone's patience runs out quicker than someone else's? — Daniel

Go to a bar, start annoying everyone, and you'll find out.

I should have thought of that.... silly me. Fortunately, you and your intelligence are here to save me from my stupidity.

I should have thought of that.... silly me. Fortunately, you and your intelligence are here to save me from my stupidity. — Daniel

The answer to each question you asked was well within your grasp, had you just thought about it and not asked. But I made the mistake of perceiving sincere curiosity and so I played along. Your sarcasm is well taken. I should have held my counsel. I'll try to be better.

Could you give examples of things that have a limit and do not occupy a space or of things that are limitless and occupy a space? — Daniel

The time it took me to write this post = 2 minutes, limit but doesn't occupy space

The number of points on a line = Infinity, limitless but occupies space

The question seems to make some assumptions that, to my reckoning, are that

1. if there's a limit, space must hold it

2. if there's no limit, space can't hold it

I responded to the challenge mathematically but that seems apposite, given a limit is given its most precise definition in math and space too, although I can't rule out a nonmathematical interpretation, is given a proper meaning in analytic geometry.

The question seems to make some assumptions that, to my reckoning, are that

1. if there's a limit, space must hold it

2. if there's no limit, space can't hold it — TheMadFool

You are right; although I am trying to look at the relationship between limits and space from the point of view of space. For example, imagine a limitless universe (a universe with no limits). Would space exist in this limitless universe if there is not a single limit*? This way it seems that for space to exist there must be at least one limit.

Do you know where I could read more about the relationship between limits and space? Is this analytical geometry?

* By limit I guess I am referring to that which marks the boundary between what's inside and what's outside (that which separates two different states/things) (honestly, I don't even know how to think about the kind of thing I am trying to talk). So, for the case of the line, I think the points cannot be limitless even if the number of them is infinite (if a line is a succession of points, each point must be a particular entity and there must be space between the points - although I understand it is said that a point has no magnitude which makes everything so much more complicated). Thus, I would say the line has a limit (it is made of points which have a limit - they are points). Now, I wanna say that time is continuous, and the time it took you to write your post is a succession of changes in space regarding your hands, other things that make you, your computer, and whatever else was required for the post to be written. The two minutes limit would then be an abstraction of your mind (that is, I do not think it is a true limit). Time is continuous and does not occupy space (although space and time are supposed to be the same thing, right - spacetime (?)). So, you writing your post could be seen as a bunch of limits changing in spacetime (no?), and the end result of such changes is the post itself. Anyways, I guess the question is: is space required for the existence of limits OR is/are (a) limit(s) required for the existence of space? kind of like the egg-chicken problem, I guess.

Space and limits have different ontologies. Limits you might say are man-made, but space is whatever it is regardless of what we say about it.

Is this analytical geometry? — Daniel

No. Limits don't usually arise in the elementary aspects of the discipline. But boundedness certainly exists for figures like circles and ellipses. However, a parabola is unbounded in the plane. Does a circle in the plane occupy space in the plane? How about a circular disc in the plane?

Does a circle in the plane occupy space in the plane? — jgill

Only relative to a reference point? (the question is genuine) I am not sure, but I would say the circle occupies a space in the plane only if a reference point (i.e., the origin of the plane - or a second circle, maybe?) is taken into account. If there is not a reference point in addition to the circle, I would say the circle does not occupy a space in the plane (as in the plane exists only if there is a reference point and a circle whose position is compared to the reference point).

or the plane exists only if there is more than one point? otherwise, it's just a point (no space)

I do not entirely agree with you. Some limits are man-made, that's true, but some exist independently of reason. Don't you think?

Hi Daniel, Can you give an example of a limit independent of reason? Actually, I suppose the speed of light is an example. Thanks!

Yeah I guess that's one. The shape of things/objects I'd say is also an example of limits that is not dependent on reason. The terminal velocity of a free falling object, the work function of a metal, the volume a sphere occupies are also examples I think. But to be honest I don't even know what to think about the question I asked in the OP. I mean, if we talk about the speed of light, if there is a limit to how fast a photon can move, does this mean a photon occupy a space (even if it has no mass)? I dunno, I guess I am confused about something.

things that have a limit and do not occupy a space — Daniel

Photon. A Photon is finite and quantised (Limited) but has no mass (cannot occupy space)

limitless and occupy a space? — Daniel

Black holes: occupy space because they have a gravitational field (due to their huge mass), limitless because of the huge time dilation caused by their gravity. Time dilates to a virtual endless standstill upon approach.

Does everything that has a limit occupy a space? — Daniel

I don't think I understand what you mean by a limit. For example the sequence 1/2, 1/3,, 1/4, 1/5, ... has the limit 0, but a mathematical sequence is an abstraction and occupies no space; although of course any physical representation of it does. So what exactly do you mean by limit?

I guess I am confused about something. — Daniel

Very few will admit that on this forum. I admire your honesty. I think you mean limits to be bounds. Do you? Like a circle in the plane vs a parabola in the plane.