Logic Puzzles: The Concept of Infinity

The concept of infinity is normally something that goes on forever, is infinitely large, or does not have limitations. When applied to a thing, the idea of infinity is limited to the said thing's properties, but alone as a concept, infinity can have several different meanings. Perhaps this is why the concept is commonly misunderstood.

Some properties of infinity that may be overlooked are the following:

1. Infinity does not have to include everything. Something can be infinitely large or repeating, and not include some trait, aspect, dimension, number, idea, etc. This concept can even work with objects, as something can be infinitely large, but only in one particular direction. An object could still be considered infinite if it is only infinitely tall. As long as one measurement keeps going, this adjective can be used (though commonly it would only be used on the particular infinite trait).
2. Infinity can exclude an infinite number of things, so long as that infinity keeps going. A negative infinity may exist with every positive one. For example, an infinite sequence of numbers can skip numbers as it goes, and if this is done at regular intervals, the total numbers being skipped is infinite as well.
3. Infinity can include the same thing, not just once, but an infinite number of times. If thinking of infinite universes (which do not exist), you yourself could be imagining such infinite universes an infinite number of times alongside an infinite number of universes where your planet does not exist.
4. Infinity can include one sole thing or measurement an infinite number of times. This includes an infinite series of 1's, or an eternal repetition of the word "zebra". All that matters is that this repetition continues.
5. Infinity can include finite things as well as infinite things within itself. For example, an array of numbers is created where the first row counts to ten, the second row counts to twenty, the third row lists the decimal numbers of pi, and the fourth row counts by two's an infinite number of times. This array may be seen as infinite since at least one of the rows inside of it is infinitely long, even though some of the other rows are finite in length. The array is also finite in its number of rows, but infinite in its number of columns – meaning both rows and columns are finite in one sense, and infinite in another, each having opposite traits.
6. The existence of infinity can create a problem where there are no limitations in potential, but there are limitations in observed actuals (the opposite can also be true, but is not a problem we could experience due to our limits of observation). If an infinite random number generator could exist, it could run an infinite number of times and never produce the number "46". In fact, it could produce "53" an infinite number of times, excluding an infinite number of numbers. In reality, this is not a limitation in potential states, but a limitation in actual states (and is certainly true when this infinite string follows the progression of time). A limitation in potential states would exist if this could not be so, further putting limits on what is actualized.
7. The finite can influence the infinite, and vice versa. Using the previous example, a random number generator could have infinite potential where all numbers are possible, but can only generate one number. Here again, potentials are infinite while actuals are finite. The opposite form can exist as well, with a random number generator that picks between ten numbers, but runs an infinite number of times. Here, the results are infinite, but the possibilities for each result are finite. Here, the opposing traits limit each other in their expression, creating a quasi-infinite/quasi-finite state as a whole.