In the context that Mycroft uses the term universe, "all of reality" is not to be equated with the items that you have listed. (Numbers, perceptions, energy, ideas and so on.) These entities belong to a part of reality, and not the whole of it. They belong to the world as we experience it and not the world as it is. The world as we experience it is analogous to the world as it is as a madman's hallucination to reality. The vision (hallucination) is inspired by a perception of reality, yet the vision of reality is heavily distorted. The ultimate reality is a single, homogeneous, entirely unlimited (infinite in all respects) entity. Our distorted perception (the world as we experience it) is finite and contains a variety of attributes such as ideas, numbers, perceptions and so on.
Mycroft's thesis: There is a fundamental distinction between the world as it is and the world as we experience it. This discovery was first established by Immanuel Kant who regarded it as the distinction between the phenomena and the noumena. He called the phenomena the world as we experience it and the noumena as the world as it is.
(Research more on Kant starting here. Kant's Account of Reason (Stanford Encyclopedia of Philosophy))
Point 1: The world as we experience it is not infinite in all respects because it does not contain a single entity that is completely unbounded. Another way of expressing this thought is as follows: the world contains many attributes and because of this, all attributes are bounded. If there was one attribute that was not bounded, than this entity would be the only thing that exists in the world.
Hence, we progress from the premise that the world has many attributes to the conclusion that the world is not infinite in all respects.
If there is a distinction between the world as it is and the world as we experience it? In other words, is there a difference between the phenomena and the noumena, or is the noumena all that there is? Hence, if the world as we experience is all that there is (and there is no noumena), then the universe is finite.
Contemporary physicists have established that the universe is finite, but is expanding. Space in particular is expanding.
My arguments are as follows.
Argument 1: Is the phenomenal world all that there is?
1. Lets assume that the phenomenal world is all that exists and the universe is finite.
2. We also know that this universe is expanding.
3. If it is expanding, then it must be expanding onto something.
4. But the universe is all that there is, therefore it is expanding onto nothing.
5. Premise 4 and premise 5 contradict each other.
6. In conclusion we can state that premise 1 cannot be true as it engenders a contradiction, therefore the finite phenomenal world cannot be all that there is.
7. Hence, the opposite of premise 1 is true---the phenomenal world is not all that there is.
Argument 2: Is the entity that is outside of the phenomenal world finite?
1. Physicists have commented that the universe is expanding.
2. They may comment only on the phenomenal world, as by definition everything that we experience is finite and not infinite.
3. Because physicists have not commented on the nature of the realm that is outside of the finite world, it cannot be known whether that realm is also expanding.
4. Since we do not know if it is expanding, one of the three following theses must be true. (1) It is finite but expanding.(2) It is infinite and not expanding, as it is not possible for an infinite entity to expand because it is all that there is. (3) It is finite and not expanding.
5. If (1) is true, then the universe that lies outside of the world as we experience it must adhere either to thesis (2) or (3). In other words, it is borrowing the material to expand onto from the infinite, noumenal world (2) or it is borrowing the material to expand onto from the large, finite world (3).
6. If (2) is true, then there is the noumenal world as conceived of by Kant. That is an infinite realm that is inaccessible to us. Our minds superimpose a perception of the world that they can perceive onto the infinite realm. Therefore there is a separation between the noumena and the phenomena. The world as it is and the world as we experience it.
7. If (3) is true, the noumenal world exactly as conceived of by Kant is false.
8. Since we cannot comment on what we cannot experience, we cannot know whether
(2) is true and (3) is false or vice versa.
9. We know that either (2) or (3) is true. Both theses entail the view that there is a distinction between the world as we experience it and the world as it is. Hence, there is merit to the Kantian view because we must purchase it either wholesale(2) or in part(3).
10. If (3) is true or the universe is finite, then it can expand only to a certain point and will contract if it expands excessively. This is impossible in the world of our experience as the law of conservation of mass states: nothing is ever destroyed complete, only changes form. The implication of this is that the universe is either (2) infinite, or (3) so large that it has not yet expanded to its very limits and begun contracting.
11. As a purely educated guess, it seems more intuitive to maintain that the law of conservation of mass will continue to hold true, or to adequately describe the work of nature. All that we know about science to this day shows that this law of nature is likely to be true and it is hard to imagine an instance where it would be false, as we have not yet seen mass being destroyed. The fact that we have not yet seen this does not show that it is impossible, yet conjecturing in favor of something that has not yet been observed is anathema to the principle of induction. In short, we cannot rule this out (just because the argument is inductively weak), yet at this point we have no reason to believe that the universe will be radically altered in the future and mass will begin to disappear. Therefore it is more plausible to maintain that the ultimate reality (the noumenal world that we cannot experience is infinite), and therefore thesis (2) is true.
Conclusion: We do not know whether the ultimate reality is finite or infinite. However, what we do know is that the world as we experience it cannot be the ultimate reality. This is the case (see argument 1) because the world as we experience it is expanding, yet if it is all that there is, it is expanding onto nothing which is a manifest paralogism. Although we do not know if the universe is finite or infinite as we lack a rigorous argument to prove the verity of either thesis, the argument in favor of the infinity of the universe is stronger than the argument in favor of the finitude of the universe. (See item 11 of argument 2)
Hence, the view espoused by Mycroft and Kant is persuasive---the noumenal world, the world as it is, or the ultimate reality is infinite and not finite.