I was curious as to whether this question has been asked or not?

we are object on a finite earth contained in an infinite universe

To answer your first question, I don't know if it's been asked or not.

As for the second, the answer is yes. Consider this "concrete" example:

Pour concrete around your object until it is inside a block of concrete. When you say a "finite space" you probably mean a space of finite volume. The concrete block has a finite volume.

Then make a mold around the concrete. The mold is hollow and it contains not only the concrete, but also your original object. The surface of the mold contains infinite points of space because a point is infinitely small.

The idea of infinitely many points is probably what you're struggling with. Even the interval on the real number line from 0 to 1 has infinitely many points. Between any two points, you can always find another point, no matter how close together they are.

RESPONSE TO YOUR EDITS:

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I see from other questions you've asked that you are an undergraduate math major. Now that I know that I will try to use more mathematical language in the following answer. Sorry I didn't do that from the start, but usually it's bad to assume that your audience knows how to do formal mathematics.

Not to say I'm right because I have higher levels of math education, but it probably bears mentioning that I have completed multiple semesters of graduate-level measure theory and real analysis coursework, as well as topology. I am quite certain that my answers are correct, and if you disagree, it is probably because of some miscommunication.

First, let me say that there are not different logical interpretations. There are only different interpretations of your definitions. The answer I am providing is THE ONLY correct logical answer based on my interpretation of your definitions.

Second, be careful with your logic. In your most recent edit, you say that trying to put an elephant in a 1m^3 box provides a counterexample, but it DOES NOT. Remember, we only have to show that there is at least 1 box big enough to put the elephant in, not that every box is big enough. To disprove this, you'd have to try every possible box and show that the elephant doesn't fit in any.

Finally, your confusion seems to lie in terminology. As the first answerer suggests, you are using the term "finite space" to mean a 3-D real space with finite volume. Such a space contains infinitely many points since a point is infinitely small. Taking the hollow object to be the boundary of the finite volume space, this hollow space also has infinitely many points.

Mathematically speaking, assuming your object is 3-D and has finite volume, and assuming that by "finite space" you mean a space of finite volume (or finite Lebesgue measure - same idea), draw a solid 3-D ball that completely surrounds your object. This 3-D ball has finite volume given by (4/3)*pi*r^3. Make sure that the ball is big enough so that no part of your object is touching the outer "edge." The boundary of the 3-D ball is a hollow sphere. Since your object is contained completely within this hollow sphere, and the hollow sphere has infinitely many points on its surface, we have done what we set out to do. The finite-volume, 3-D object contained inside the finite-volume, 3-D solid ball of radius r is contained within the hollow sphere, which has infinitely many points.

This is the best I can offer without actually taking the time to prove to you that the hollow sphere has infinitely many points.

Mathematically speaking, yes. "Contained in a finite space" usually means it can fit inside some sphere with with a certain (finite, possibly very big) radius. That sphere (or any other, no matter how small the radius; excluding the degenerate case of radius zero) contains infinitely many "points of space", i.e. triples of numbers (x, y, z) that satisfy the inequality that describes the interior of the sphere.

Whether or not this is the true nature of the universe is an unanswered question so far... i.e. we do not know if space is really continuous or discrete. Can you truly (assuming infinite precision in your instruments, etc.) keep dividing an area into smaller and smaller bits ad infinitum, or do you eventually get to a scale at which it doesn't make any sense to go smaller... Most of our mathematical models of space assume it's continuous, and work well for our purposes. But they're just models in my view and don't really answer this question.

Even the smallest space in three dimensions contains an infinite number of points. If an object can be contained in a finite space, it may still be unable to fit inside an object that contains infinite points. That's because any three-dimensional space has the property of having infinite points, so the second object may still be smaller than the first space.

yes it is, because the two concepts are different.

Theoretically, there is a point between any two points. So take any object. Say a 1 foot long ruler. It obviously fits in a finite 3d space, say a big shoe box.

Now, treat that ruler as a number line. Take any two points on the line. There is a point in between. Keep doing that for ever. There are an infinite number of points on the object (even though there are a finite number of atoms, but there is space between the atoms).

umm no because they are both infinitive space so that means you couldnt, like if a box was a 4 by 4 and you wanted to place another 4x4 box it wouldnt go in becuase they have the smae measurements'