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An entity can be infinite to its "left" ? and bounded on its right. Moreover, finiteness can exist where no boundaries can. Take a sphere: it is finite, yet we can continue to draw a line on its surface infinitely. The "boundary", in this case, is conceptual and arbitrary: if a line drawn on the surface of a sphere were to reach its starting point ? then it is finite. Its starting point is the boundary, arbitrarily determined to be so by us.
This arbitrariness is bound to appear whenever the finiteness of something is determined by us, rather than "objectively, by nature". A finite series of numbers is a fine example...
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