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There always ewisted a universe

Using a complicated mathematical axiom with space, I found
the following :
Affter an infinite time, there will be a Big Crunch (collapse of
the universe) followed directly by a Big Bang and again after
an infinite time another Big Crunch and so on...
There always existed a universe and people should not talk
of the creation of the universe.
Adib Ben Jebara.

Infinite time, do you think?

It means never - and such event would never occur, after then.

About the very numerous

Mr Andreas Blass was kind to clarify the following about alephs:
The alephs are a proper class.
The alephs are indexed by ordinals such as omega, omega+1,...
2 omega,...
Alephs are cardinalities of well orderable sets.

Let us consider the ordinal corresponding to the cardinality of
the set of real numbers, with the notation c.
Let us consider the aleph indexed by c, the alephs smaller than
that one would be as numerous as the real numbers.
One should start to feel some dizziness from the very numerous.

Let us consider the ordinal corresponding to the cardinality of
the set of subsets of the set of real numbers, with the notation
s.
Let us consider the aleph indexed by s, the alephs smaller than
that one would be more numerous than the real numbers.
Aleph indexed by s is itself big beyond imagination. It is
difficult to get an intuition of it.
Such an aleph appears almost never in mathematical texts.
Physical space could not have the dimension of such an aleph (I
explained in "Physical space is infinite", in ASL Winter Meeting
2006 2007, why physical space is infinite).

So, for what could be used a very big aleph ?
May be the number of Big Bangs, each associated with a previous
Big Crunch, is infinite and a very big aleph, as it probably never
ends (although it takes an infinite time for a Big Crunch to happen).
Indeed, it is in the fields of cosmology and cosmogony that we can
hope to find use for the very big alephs.
I think there was no beginning for the cosmos, it was always there
and that is why very big cardinals should be used to study the cosmos.
Adib Ben Jebara

we can't be certain of either theory though, one day we might be, but for now we cant draw any conclusion

but how would the universe have enough energy to sustain itself infinitely? i mean, eventually (according to the second -or is it third?- law of thermodynamics) all processes grow towards chaos, and energy is lost or at least not usable. and there is dark matter, etc.
and if it was infite, how did it ever come into being? because it obviously did, as we're in it right now.

There are singularities that the part of the theory we know does not handle well.
The universe has no beginning and no end, it is from one universe to another.
Adib Ben Jebara.

We aren't required to be sure of some theory, but the probability calculus enables us to determine, which solution can be more probable, then others. Maybe we should forget the finiteness of Universe at all and we should concentrate just to the most probable explanationa available.

from the theory of relativity it seems plausible for there to be an edge to the universe and the universe being of a finite size (having to do with time dilation).... as for an infinitely dimensioned universe etc etc, i don't know what field of science could have possibly 'determined' that the universe was of infinite age...

Zephir,
Thank you for your reply.
big fat pig,
Theory of relativity does not explain the singularite of the Big
Bang but set theory can.
Adib Ben Jebara.

We can compare the reality observation to the situation, when observing a laser ray through inhomogeneous atmosphere. If the environment would be completely homogeneous & clear, we would see nothing. If the atmosphere will be too cloudy and foggy, we would see the laser ray, but we wouldn't see too much as well.

So here exists an optimal density (and geometry, too) of environment fluctuations, which would enable us to see as much from the neighborhood, as possible. The vacuum is such environment.

But as we can see, the ability to see at least something is always connected with existence of some insintric inhomogeneities of the environment, which are result of the dispersion on both sides of the transparent region of electromagnetic spectrum. And the light will be always bended with the distance, and after certain distance limit, the level of light bending will achieve the limit of total refraction - the light will not be able to pass through space anymore. This is the boundary of Universe, which you have talked about.

Note that by this interpretation the Universe boundary is arbitrary - if we would travel towards it, it would recede accordingly. It doesn't say anything about physical boundary of Universe, it's just "visibility distance" limit.