Intelligent Life in the Universe

If the universe is infinite, must there exist infinitely intelligent beings in the universe?there are infinite planets with infinite environmental conditions, each environmental condition exists on infinite planets and infinitely many of them have life on them. These lifeforms must have infinite levels of intelligence. if we were to create a sequence of every being in the universe's IQ and did not repeat identical results, the sequence would be 1, 2, 3, 4..... , infinity. I may have misunderstood the limits of how infinity can be used, but this seems to make logical sense. There are infinite infinitely intelligent beings in the universe. Also there are infinite civilizations out there, each being infinite times more powerful and technologically advanced than humanity. The universe has no beginning, meaning at has existed eternally. Untold unlimited species and civilizations have existed and died out long before the earth was even formed.

I am editing my answer to reflect the desire of the person asking of treating this as a hypothetical question, assuming the premise to be true, in a "what if" fashion.

So if the universe was indeed infinite, then it has the potential of having an infinite number planets; however you have to have in mind that planets were not forever there and therefore time is necessary for a planet to form around a star.

So if you let enough time go by (have in mind that Earth is around 4.5 billion years old at the moment). then potentially, there would be an infinite number of planets in the universe.

After that you mention that there would be infinite environmental conditions. Even in an infinite universe that is not necessarily true. The environmental conditions in a planet are due to the size, composition, age and geological processes inside the planet. So the number of possible environmental conditions are not infinite, they are limited by the number of combinations allowed by the rules that govern the universe. In order to understand this better, you can imagine for example an infinite list of binary, two digit numbers. Even if the list is infinite, the truth is that you will only be able to find 4 unique number combinations: 00, 01, 10, 11 and the infinite list is simply formed of repetitions of these numbers. Of course this analogy is an over simplification and there will exist much more possible combinations that may form planets in the universe, but they are certainly not infinite because the rules that govern the universe will only allow for some of them.

As I said before, even if the universe is indeed infinite that does not mean that all the planets are potentially there. Following the same analogy, imagine that the list of two digit binary numbers that represent the planets, one is added every second. That means that potentially, in the distant future there will be an infinite number of items on that list, but they are not there already, they need time to appear. Infinite time, actually.

So in order to form an infinite number of planets it is necessary an infinite period of time.

Now say, for example, that the number generator tends to repeat number 11 more often than the others. So for every one instance of 00 there will be 10,000 instances of 11. I introduce this variable because we know, for example, that is possible that planets like Jupiter and Saturn are much more likely to form around a star than planets like Earth or Mars. If this is the case then even though there will be eventually a infinite number of planets, there is a chance that only a small fraction of those are suitable for life.

So it may be that for an infinite number of planets suitable for life to exist, much longer is required than for an infinite number of planets where life is not suitable.

An finally, life, in the simplest form, is much more likely to appear than intelligent life. And the separation between the chances of these two to appear is too big in magnitude. Taking the same analogy again, if 00 is suitable for life and all the other combinations are not suitable for life, then probably there will be only one 00 in a sea of millions of non-00s.

If to all that you add the fact that intelligent life is not eternal, and that they may disappear at some point, it is possible that even in an infinite universe, with an infinite number of planets, two intelligent forms of life never overlap in the same period of time, even in an infinite period of time.

So even if potentially, an infinite universe is hypothetically able to eventually spawn an infinite number of intelligent forms of life, it is also likely and possible that not even two of those ever even co-exist.