From this investigation, I have managed to answer all the questions I wanted to answer. I did want to know what happens when I take away octonions and quaternions from the 0,1 interval, but I did not really understand the concepts of otconions and quaternions, so I decided to leave it out. Also, I think I already had too many words, so I did not want to overload my IA with too many words.
Also, I did realize that ∞−∞ is a little too conceptual to use for anything in real life. So I could not apply this to anything. But, I did try to come up with different cases to show that ∞-∞ is undetermined.
I did try to come up with real life situations where I use the concept of infinity, but I only came up with the L’Hospital’s rule and I figured talking about the L’Hospital’s rule would only be me decreasing the concept of L’Hospital’s rule not applying the concept to real life problems.
I also thought I could try to use …show more content…
From reading those sources, I started to wonder, “Are there any infinities bigger than the natural numbers but smaller than the real numbers?” If so, the infinity of the real numbers would be bigger than aleph-one. But, after a little more research, I found that “The continuum hypothesis asserts that ℵ_0=c, where c is the cardinal number of the "large" infinite set of real numbers (called the continuum in set theory). However, the truth of the continuum hypothesis depends on the version of set theory you are using therefore, it is undecidable. So to make things simpler, I decided to use ℵ_(1 )as the cardinal number for the set of real numbers because according to the continuum hypothesis, ℵ_(1 )corresponds to the number of real numbers, and I thought tat was good