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# Conceptualizing the Mathematical Notion of Infinity Through Radioactive Decay

The mathematical notion of infinity can be conceptualized in many different ways First as counting by hundreds for the rest of our lives an endless quantity It can also be thought of as digging a whole in hell for eternity negative infinity The concept I will explore however is infinitely smaller quantities through radioactive decay Infinity is by definition an indefinitely large quantity It is hard to grasp the magnitude of such an idea When we examine infinity further by setting up one-to-one correspondences between sets we see a few peculiarities There are as many natural numbers as even numbers We also see there are as many natural numbers as multiples of two This poses the problem of designating the cardinality of the natural numbers The standard symbol for the cardinality of the natural numbers is o The set of even natural numbers has the same number of members as the set of natural numbers The both have the same cardinality o By transfinite arithmetic we can see this exemplified 1 2 3 4 5 6 7 80 2 4 6 8 10 12 14 16 When we add one number to the set of evens in this case 0 it appears that the bottom set is larger but when we shift the bottom set over our initial statement is true again1 2 3 4 5 6 7 8 90 2 4 6 8

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