# Who said the Universe had a beginning?

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2 hours ago, J.C.MacSwell said:

The surface of a sphere is borderless...yet finite.

No - a sphere has a border.

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9 minutes ago, Gater said:

No - a sphere has a border.

The surface...

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13 minutes ago, Gater said:

No - a sphere has a border.

Enlighten us what you mean since I don't think you are correct, in strictly mathematical terms.

But then neither are those who talk about the surface of a sphere either.

Edited by studiot

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24 minutes ago, zapatos said:

The surface...

All spheres have borders - think of the earth, its a sphere - isn't there a border between the ground and air?

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41 minutes ago, Gater said:

No - a sphere has a border.

Really? Where is the end of the world?

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What does that mean?

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2 minutes ago, Gater said:

What does that mean?

Who are you addressing? What does what mean?

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Note, strictly a sphere is not a solid object.
A sphere does not have a surface, it is a surface.

The correct mathematical term of the solid object is a ball, but there is much more to it than that.

There is also mathematical justification for this,

13 minutes ago, Gater said:

think of the earth, its a sphere - isn't there a border between the ground and air?

But it is not what you think.

Being a true surface a sphere has two sides.

An inside and an outside, with inward and outward normals.

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3 minutes ago, Strange said:

Who are you addressing? What does what mean?

You -  you wrote where is the end of the world

2 minutes ago, studiot said:

Note, strictly a sphere is not a solid object.
A sphere does not have a surface, it is a surface.

The correct mathematical term of the solid object is a ball, but there is much more to it than that.

There is also mathematical justification for this,

But it is not what you think.

Being a true surface a sphere has two sides.

An inside and an outside, with inward and outward normals.

A sphere can be solid or hollow

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16 minutes ago, Gater said:

All spheres have borders - think of the earth, its a sphere - isn't there a border between the ground and air?

We are talking about the surface of a sphere (the surface of the Earth, if you like). Or, as studiot correctly points out, a sphere.

A sphere (the 2D surface) does not have an edge, border or boundary. It is a continuous, unbounded surface with a finite area.

If you are unable to understand this simple mathematical (and practical) fact, I am not sure why we should take your random assertions too seriously.

2 minutes ago, Gater said:

A sphere can be solid or hollow

A sphere is a 2D surface.

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2 minutes ago, Strange said:

We are talking about the surface of a sphere (the surface of the Earth, if you like). Or, as studiot correctly points out, a sphere.

A sphere (the 2D surface) does not have an edge, border or boundary. It is a continuous, unbounded surface with a finite area.

If you are unable to understand this simple mathematical (and practical) fact, I am not sure why we should take your random assertions too seriously.

A sphere is a 2D surface.

A sphere is 3d - dont you get that?

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6 minutes ago, Gater said:

A sphere is 3d - dont you get that?

It isn't, mathematically. But even if we go for the informal definition of a sphere as a 3D object, the surface is two dimensional with a finite area and no boundary.

The surface of the Earth, for example, is two dimensional and does not have an edge. Unless you are a flat-earther and think that you will fall off the edge if you try and sail all the way round.

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You want to explain how a basketball is 2d?

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2 minutes ago, Gater said:

You want to explain how a basketball is 2d?

Because we aren't talking about the insides of it, or of the Earth, just the surface.

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All spheres are 3d - look it up in a dictionary - unless you live in fantasyland.

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6 minutes ago, Gater said:

You want to explain how a basketball is 2d?

The SURFACE is two dimensional. Do you know what "dimension" means? DO you know what "surface" means? Do you know what it means to be two dimensional? Apparently not.

1 minute ago, Gater said:

All spheres are 3d - look it up in a dictionary - unless you live in fantasyland.

"a sphere ... is a two-dimensional closed surface embedded in a three-dimensional Euclidean space"

A surface is two dimensional.

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height - width - depth - 3d - all spheres are 3d

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Just now, Gater said:

height - width - depth - 3d - all spheres are 3d

Simply repeating your false assertion won't magically make it true.

A dimension can be defined very roughly as the number of bit of data needed to define a location. So, in 3D space you need 3 bits of information: x, y, z for example. In 4D spacetime you need four bits of information: the three spatial ones plus time.

On the surface of a sphere you only need two numbers (latitude and longitude, for example). That is why the surface is two dimensional.

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1 minute ago, Gater said:

All spheres are 3d - look it up in a dictionary - unless you live in fantasyland.

This seems like you're purposely trying to misunderstand. When you're talking about the SURFACE of a sphere, you're only talking about two of its three dimensions, OK?

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24 minutes ago, Gater said:

height - width - depth - 3d - all spheres are 3d

But if you stand on the surface of a large ball and you are not allowed to jump or dig, where can you go? To your local left, right, back, forward. Two dimensions, not three.

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1 hour ago, Gater said:

All spheres have borders - think of the earth, its a sphere - isn't there a border between the ground and air?

The Earth is actually an oblate spheroid. But tell me, what is North of the North Pole?...Or South of the South pole?

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1 hour ago, studiot said:

But it is not what you think.

Being a true surface a sphere has two sides.

An inside and an outside, with inward and outward normals.

In you obstinancy to turn a deaf ear to others who are offering the simplest, yet perfectly sound, scientific/mathematical explanations you have missed this very important point, which I made earlier.

An n dimensional sphere is the set of all the accumulation (or limit) points of a closed ball in an (n+1) dimensional manifold.

An important property of surfaces is that they divide the manifold into two parts.

For a sphere these are the inside and the outside.

Edited by studiot

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!

Moderator Note

My obtuse-ometer has pegged high. Five unsuccessful tries at “we’re talking about the surface” is a sign that we’re done.

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