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No best answer has yet been selected by Kishimo. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.It is possible for the universe to be finite in size and for it not to "stop" anywhere. It doesn't have to have any edges. It might be the 3-dimensional surface on a 4-dimensional hypersphere (i.e. curved round).
What this means is that if you blast off in a rocket into outer space and carry on for ever, you will eventually find yourself going back to Earth from the other side (just like an explorer going round the world will eventually get back to the continent he started from) without falling off any edge and without having changed direction.
Following on from Bernardo, imagine explaining to someone from a flat 2-D world how the earth works. He couldn't imagine walking in a straight line and ending up where hw started from, whereas we can easily.
The universe is similar in that it has an extra dimension that we can't easily comprehend. If you kept flying in a straight line you would eventually get beck to where you started.
The universe is constantly expanding, therefore it must be finite.