Can the Universe be infinite in all directions, yet still have been created in a Big Bang?

It is not illogical, after all infinity is a tricky thing, The universe is infinite in all directions, not only above us in the large but also below us in the small. If you think of the universe of coming from nothing then it will not make sense to you, because the big bang was the work of quantum mechanics, and in quantum mechanics there is no such thing as nothing. Just because the universe came from a point does not mean that the point was not infinitely small, which means that the universe is infinite and it is not really illogical.

My favorite interpretation is that space is expanding, and unending, but not infinite.

There is no end to be found. It's a step up in dimensionality from the idea of crawling on the surface of a balloon. No end can be found; the surface has no end. The balloon's surface can be expanding and unending, but not infinite. The surface of the balloon is the frontier of its expansion.

So from a strictly three-dimensional point of view, you can go in a straight line forever in space and never find an end, although you will end up re-tracing your path eventually.

In a 3-dimensional view, the universe has no end or edge, and no center. From any part of the universe, far galaxies are moving away at a speed depending on their distance.

From a 4-dimensional view (4 spatial dimensions, not 3 spatial dimensions plus time), our whole 3-dimensional space IS the three-dimensional-edge (frontier) of the expansion.

The Big Bang did not start in a "point".

In classical General Relativity, the Big Bang (specifically, the Friedmann solution to the Einstein Field Equations) starts with a singularity. The Universe can in principle be infinite for all times after time zero. It could also be finite --- we don't know the boundary conditions.

In reality, quantum gravity effects (that we don't yet understand) probably prevent the initial Big Bang from being true singularity.

I like to think of it this way...

The Big Bang theory's main point is that we noticed an expansion occurring

If we rewind things, an expansion becomes a contraction

Up until the mysterious primordial particle containing everything

The idea of the universe being infinite is that it will not stop expanding, it will continue to expand forever.

What exactly it is expanding into, is unfathomable at the moment...

You might also want to look into other theories, such as the Big Rip/Crunch/and Bounce theory. Interesting subjects to study...

space is infinite. the universe is not. What, you think that theres just big wall of nothingness dictating the edge of spaces? But like many things in science, that question cannot be answered. We have absolutely no way of traveling to the edges of the universe, and therefore we cant tell what lies beyond that. But the universe is finite. But where we dictate the end of the universe lies is another matter. Some say the universe is inifinite and includes that which lies beyond the known universe that resulted from the big bang .I say that what originated from the big bang is the universe, and whatever lies beyond is a multiverse to me.

Yeah, but there probably never was a Big Bang though. A static, eternal universe makes more sense. This documentary may enlighten you...

http://www.youtube.com/watch?v=1yTfRy0LTD0&playnex...

It isn't the space between the galaxies that is expanding. It is the distance, or space itself that's going out. With or without matter.

NO! The universe is just unbelievably vast to us unknowingly tiny humans.