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Saturday, December 16, 2017
Article written by Joe Pagano

Concepts In Infinity – Some Ideas To Ponder

In my series of articles entitled Dabbling in Infinity, I talk about the existence of different realms of infinity and how we can establish this as an irrefutable reality. Did you ever seriously consider this idea of infinity? According to any dictionary, infinity is that state or quality of being infinite. Infinite means boundless; having no limits or end; immeasurable. Now I ask a simple question: How could God not exist if something such as infinity does exist? Indeed, how could we have a mind to comprehend a concept as daring as infinity if an infinite mind such as that of God did not give us this power? As Voltaire, the author of the French classic Candide said, “The creation betokens the creator.”

Yet if the above statements are not enough to drive home this point, consider some curious facts about the set of counting numbers, that is the set {1, 2, 3, ...}, which goes on forever. Now consider the idea of exponentiation or raising a number to a power. For example the number 2 to the second power is equal to 2 times 2 or 4. The number 2 to the fourth power equals 2 x 2 x 2 x 2 or 16. The number 2 to the hundredth power equals 2 x 2 x ... x 2 one hundred times. This number is larger than the number 1 followed by thirty 0's. Now that’s quite a large number. Yet the set of counting numbers is far larger than the number represented by 2 to the hundredth power. Far larger.

You see, we could take this number and raise it to the one hundredth power. And then we can take that result and raise it to the one millionth power. And... You get the point. You are talking about numbers so large that the number of atoms in the entire universe pale in comparison to a tiny fraction of the number of elements in this set. In fact a fraction—however small—of infinity, is still after all infinity!

There is a curious limerick on infinity, that goes like this:

There once was a student from Trinity,
Tried to take the square root of infinity,
Whilst counting the digits,
Was seized with the fidgets,
Gave up math and took up divinity.

You might remember from your astronomy days that the vast distances in space are measured in light-years. The speed of light is 186,282 miles per second. A light-year is therefore approximately 5.8 trillion miles. The distance between earth and some far away galaxies is measured in billions of light years. Yet this number in terms of miles would be a very inconsiderate comparison to itself raised to the one hundredth power; and yet the set of counting numbers is home to this monstrous number as well as much bigger monsters than these! How big is this set you might ask?

Think of the most amazing computer that ever existed or will exist. This computer can do any calculation that you could dream possible. Such a calculator has a brain that could do such calculations as the ones mentioned in the previous paragraph in the whiff of a millisecond. Suppose you let this calculator do the following task: you let it run for one year non-stop and its task is to repeatedly raise the result of its previous calculation to the same power. Thus if the calculator got an answer of one billion, let us say, then this machine will raise one billion to the one billionth power, and so on. Let’s assume the machine can do each such calculation in one second. We let the machine run for one year and then observe the final stupendously gigantic number.

As big as the unfathomable result above, we still have a number which does not even come close to being the biggest number in the set. So how big is infinity? As big as the mind of God. That’s how big.

See more at Dabbling in Infinity and Math by Joe
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