This video shows all the different reasons why .999 = 1

Why Every Proof that .999… = 1 is Wrong

Tries to joke that .999 is not equal to 1. Shows why some techniques cant be used as an april fools joke.

The Calculus of Bad Driving

Driving slower doesn’t really help as much as leaving space between cars when it’s raining. This it because it takes longer for cars to decelerate to a full stop and the distance plays a greater role

I choose this video “9.999… reasons that .999… = 1”

This video shows all the different reasons why .999 = 1

Since I find it the most interesting I felt intrigued as well as somewhat dissatisfied about my original intuitions about the number .9999

I learned that most mathematicians define .9999 as equaling 1 since the rest of the arithmetic just works.

One question I have is that I wonder for what applications would having .999 not equal to 1 make it easier to use.

I believe this lesson shows an aspect of math that many people may not be aware of. That mathematics doesn’t need to have exact definitions and that definition variations based on application may simplify computation. Such as the invention of the imaginary numbers. Or in this video showing that .999 is equal to 1.

]]>I agree we should always be prepared. But even if we are not prepared we should be aware of what we are missing and how much we need to catch up on. That way we can make up at-least some work that we are missing.

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What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)

Based on this advice, what changes can you make right now to help you succeed in this course?

The most relevant pieces of advice are the following:

“Be organised and take note of the checklist Professor Reitz writes on the right side of the board (and Openlab)”

“Do all of the WebWork, there is a surplus that counts for extra credits should you need a fallback.”

” Seize every opportunity for extra credit that Professor Reitz offers, and he offers a lot!”

I didn’t realize that WebWork makes up such a large percentage of our grade and I should’ve be taking advantage of it.

I agree with you Sonam, a that’s a very interesting story.

The best way to learn is to visualize and be able to clearly translate. Then you can derive the formulas instead of memorizing them.

Another benefit is that you will know your derivation may be more reliable then your memory.

While taking math and science classes in highschool together… I saw the same techniques being used to solve a wide variety of problems. From that moment forward I wanted to learn all the different techniques.. Cause Each technique means hundreds if not thousands of applications.

Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college). Describe what happened. Do you think you could explain it to others in a way that they could have the same flash of understanding?

Once when determining triangle congruence I visualized the the angles and determined why certain properties such as SAS ASA have to indicate congruent triangles. If a single angle or side length is changed it changes the whole triangle. I believe this is very easy to show to others using a chalkboard or even a model of sides with hinges to demonstrate varying angles.

]]>That is very true Sonam. Plus to add to what you’ve said. The definitions of certain terms may vary. Such as the Set of Natural numbers some definitions may Include 0 in the set while others don’t. Your past usage of these terms may lead to confusion.

]]>One important prior knowledge that I believe you need to understand it very well in order to succeed in this class is “List of types of numbers” specially if you took middle and high school in another country. Because when you doing proofs, You need us the definitions of different types of numbers, in order to clear what specific types of numbers you are talking about. Even in the class Prof.Reitz will provide you the definition of Types of number. But it will be just a reminder you need understand then concept of them before you take the class. Following are the types of numbers will be most important for this class: Odd/Even numbers, Prime numbers, Real numbers, Natural numbers, Integers, Rational numbers, and irrational numbers.

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