2012 Spring – MAT 1575 Calc II – Reitz

The Powers of 10

Infinity means something that has no ending. Something that goes on and on without any limits. I don’t know exactly at what age I was introduced the idea of infinity, however, in the early ages, I was introduced the idea of God being infinite that God has no beginning and no ending, and He is the everlasting. When I was young, from religious perspective, I knew what infinity is, but I didn’t really understand the concept of infinity until I faced calculus in High School.

In mathematics, “infinity” is not a real number, it’s a symbol. When some numbers or series goes forever and ever, we say that it’s an infinity. I took a picture of a leaf. Now, we will take a trip by digging into the leaf, reducing the distances of travel by factors of 10. With the factor of 1o, we will see the mechanism of a single leaf/matter goes to infinity.

10^0 is our starting point which is a distance to a bunch of leaves in the garden. 10^-1 is getting closer at 10 cm. We can delineate the leaves. At 10^-2, it is possible to observe the structure of the leaf. At 10^-3, the cellular structures start showing. At 10^-4, the cells can be defined, and we can see the union between them. At 10^5, start our trip inside the cell. At 10^-6, the nucleus of cell is visible. At 10^-8, in this micro universe the DNA chain is visible. And it continues up to 10^-16. After this nowhere more to go at the limits of current scientific knowledge. After this, if scientist come up with more information about this matter, still this process has no ending. As a result, it goes to infinity.

The idea of powers of 10 from micro to macrocosmos was also introduced in the short film “Powers of 10” by Charles and Ray Eames. This film could also be found on Youtube.

I wanted to create a forum where students can help other students who are having trouble with the WebWork problems. I don’t know why this hasn’t been done before, but it’s never too late to ask for help.

I also find it particularly annoying to keep going back to the OpenLab Homework Assignment #4 post to get the link to log into WebWork. Hopefully, most of you are smarter and just made the link a bookmark or a pinned tab in your browser but, if you haven’t, clicking any of the webwork links or webwork icons above will take you there. You can also right click any of them and select “Copy Link Location”, to get the url and save it somewhere.

I’d say, as far as asking for help goes, try to use in your queries. It makes it easier for others to understand what you’re asking, so help them help you. But I also understand that it’s difficult to get the coding right sometimes so just try your best. And, if it doesn’t work out, express the problem clearly with plain text in a reply.

And, this kind of goes without saying but, Mr Reitz can obviously read this so it wouldn’t behoove you to flat out ask others for answers on here. And, if that happens, this post will likely get deleted. So with that in mind, use it as you will.

Hope this helps.

What exactly is infinity ?

Infinity is a difficult concept to grasp fully and it is crucial when learning calculus. Infinity does not play a role in our everyday lives. We are finite and living in a finite world. Our lives have definite beginning and endings.

To grasp some sensory experience of infinity is to gaze toward the heavens on a beautiful sunset evening. This picture shows that the sun is infinite, boundless and undefined. It remains an open question, whether the universe actually extends forever. Infinity remain untouchable in its perfection.

Infinity, by definition, is the notion of something that has no end.  Something that does not grow, but something that is fully formed.  I believe that infinity is something that is not attainable, but yet its something we strive for.  We strive for a very great amount or degree (whatever that may be).  Also to be continued indefinitely.

I can’t exactly remember when I first came across the notion of infinity, probably when I was about 5 or 6 years old when Toy Story came out.  Buzz Lightyear shouted the famous “To infinity and beyond” quote.  More notably, I heard it on a rap song called ’93 ’til Infinity by Oakland based hip-hop group Souls of Mischief.  Although the song has absolutely nothing to do with Math, the context basically deals with their daily lives.

The picture you see is a view of the Verrazano-Narrows Bridge, which connects Brooklyn and Staten Island. I believe this image represents two points which continues on far beyond the pictureitself without a specific end.  With that said, the farther you go, you’ll end up with a different result (or in this case, location) every time.

sky

What is infinity? To me infinity is an idea of something that has no end. In mathematics we know that infinity is just some big endless number, but what do we think of infinity in reality? Well to me I just have to look to the sky, our universe, and I can firmly believe that it is boundless. I believe it was when I first started learning to count and doing algebra was when I discover about the term “infinity”. I usually just think it is some huge number that stops somewhere, but as I grew up more and become aware of what it is, I finally took up the idea that infinity is just something that has no limit. It is endless.

The picture I posted was taken by me on a beautiful clear sky. The sky is just basically the space vacuum of the universe, and when we think of the universe it has lots of stars and systems and galaxies that we just assume is infinite. At least to me that is what I think of the universe.