In my science class I was taught that the definition of matter was: Anything that has mass and takes up space.

I was also taught that the definition of mass was: The amount of matter something contains.

 

If we place the definition of mass into the definition of matter we get: Anything that contains matter and takes up space.

This is a circular definition. One rule of definitions is that they can't be circular.

Can anyone tell me the real definitions for these terms?

In my science class I was taught that the definition of matter was: Anything that has mass and takes up space.

 

Ok, so this is a reasonable starting definition of matter. However, as far as I know there is no completely agreed upon definition. Even more loosely, matter is what physical objects consist of; atoms, electrons, protons, neutrons, quarks and so on...

 

I was also taught that the definition of mass was: The amount of matter something contains.

 

Mass is a property of matter and roughly you think of this as the amount of "physical stuff".

 

Like I said, there is no completely agreed upon definition of matter and it becomes even more complicated when quantum theory comes into play.

Time is missing from your definitions.

Time is missing from your definitions.

 

You would like to define matter as "some physical object that has mass, occupies a non-zero volume and has a non-zero duration"?

 

I think for classical mechanics and similar this would be on ok definition. So on macroscopic scales I am sure this would be ok. In everyday life this is what one would mean by matter.

 

You could the argue if a particle is matter or not, but as that is an idealised useful mathematical tool I would not worry too much about that.

Something like that. Mainly because Space alone has no meaning under Relativity.

I always have the feeling that Time is very easily forgotten.

 

We know as a definition that matter occupies a certain amount of space.

We know that to travel any amount of space, matter needs time.

So we can conclude that matter needs time in order to occupy space.