In ordinance with general physical laws, one being relativity stating the limited earth, common sense like the fact that we can't even imagine reaching the end of it, and standard facts such as a star being about 33 billion miles away from earth, it is arguable (as of now) 99.9% likely that space is UNlimited. Oh and, a satelite alone is proof it exists. Technically 'empty space' does not exist, although.
The limitless size of space is some thing why it and my dick have so much in common, if you'd like to see further proof.