Personal Search for Infinity

My personal interest in infinity began when I was young. I was always a kid that asked why? I would ponder long spans about things that I could not comprehend, such as flight, space, stars and wars.

One concept I could never get my arms around was infinity. When I was told the universe had no boundaries, I became very intrigued. I also became intrigued when my early math teacher told me that any real number added to infinity or subtracted from infinity (besides infinity) would result in infinity. These answers never made sense.

Through the years, I casually explored these concepts. I learned that the universe is indeed finite. Science has proven that the universe is expanding. However, the universe cannot expand unless it is finite in size (http://en.wikipedia.org/wiki/Universe). I also learned that infinity can have a limit and can be expanded or contracted.

For example: The range of "5 to infinity" has a lower limit of "5". However, the range of numbers is still infinite. This infinite range can be expanded by 4 if we reduce the lower limit to "1" resulting in the range of "1 to infinity". Both ranges are infinite, but both have different "cardinalities".

A cardinality is defined by the Free Online Dictionary of Computing as:

The number of elements in a set. If two setshave the same number of elements (i.e. there is a bijection between them) then they have the same cardinality. Acardinality is thus an isomorphism class in the category of sets.aleph 0 is defined as the cardinality of the first infinite ordinal, omega (the number of naturalnumbers).

This perplexed me and began my quest to understand this amazing mathematical concept. I will delve into the concept of cardinality (hence the title of my blog) in my next post.

References:

cardinality. (n.d.). The Free On-line Dictionary of Computing. Retrieved November 17, 2006, from Dictionary.com website: http://dictionary.reference.com/browse/cardinality