Numbers chapter 1

"It's much easier to write 1, so that's what we usually do. But we can write some ideas using different words..."

Without this idea, math would be a whole different thing. People rewrite numbers in order to simplify, factor, and solve many problems. One such example uses trigonometric identities. In order to prove x is equal to y, the idea that something can be rewritten into a different form proves to be a great tool. When computing algebraic equations, adding "1" to both sides can open up the problem to new paths one can take to solve it. I know that people have a hard time understanding that 1 is a useful tool that everyone uses.

Numbers Chapter .00000000001

"Once we could write tiny numbers as fractions and as decimal fractions, a whole new world was opened to us."

As we advance to the future, nanotechnology's role in society will grow. With the whole "Smaller yet better" market increasing, nanotechnology is the solution for this demand. The reading mentions how transistors are getting smaller, and are making microchips process data faster. From vacuum tubes resulting in huge computers to transistors resulting in small microprocessors, we have came a long way in a short amount of time. If this keeps up who knows what can be done with nanotechnology. Maybe it can be integrated with the ideas of genetic engineering, or create mechanical solutions to problems surrounding the human body.

Numbers

"Using this argument, it's simple to show that zero divided by zero could be anything at all! The answer is indeterminate."


I've wondered if the words undefined and indeterminate were interchangable. When indeterminates were talked about this in class for the first time, it seemed that they were just a bunch of expressions that couldn't have an answer. I soon found out that they were expressions that did have answers. It's just the issue of which answer is the correct one. You can have an infinite number of ways of writing 0/0, but in the end, its still just 0/0. It's makes me think of all the different ways we can write numbers and expressions. The idea that problems can be rewritten is an essential skill required for problem solving. If something doesn't look familiar to you, rewriting it into a form you have learned to deal with can help you solve the problem. Since 0/0 is one of many indeterminates, I wonder what methods are out there to solve the other ones in the math world.