So far, using gravitational lensing, and the HST, we have seen images of galaxies as they were less than half a billion years after the so called Big Bang.
Of course, the further we see into space, the further are looking into the past.
But as the Universe has a finite age, is it reasonable to say there is only so far we can possibly see into the observable Universe?
If so, what do you think you will see, at the limit?
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No. The number of things we can see increases as time passes. There will never be a conflict. For example, when the universe turns 14 billion years old, we will see things that are around 14 billion years old. The observable universe grows at the speed of light, and the universe expands at an accelerating rate which is faster than that.