An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math.
Music: Legions (Reverie) by Zoe Keating
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Have you ever failed at something in your life? I’ll bet that you have. All of us have and it’s nothing to be ashamed of. Failing is perfectly normal.
Many of us went to school and were actually punished for making mistakes. Now you may find it hard to believe, but it really is impossible to succeed unless you have first failed. That is, as long as you are willing to learn from your mistakes.
You see, if you try to do something and it doesn’t turn out as you’d expected, you’ve still succeeded. You’ve successfully learned that what you did was not the way to get what it was that you were after.
Failing, in and of itself, is an integral part of the learning process that we, as human beings, must go through in order to advance ourselves in life. The challenge isn’t in the process of failing, or making a mistake, it’s in how we were trained to respond to our mistakes.
Most people will try anything once. If they fail, they will likely never try again. Or, if they do try again, they won’t let anybody know about it!
Many of the most successful people in our society today have failed many more times than they have succeeded. The only difference between them and you is that they kept at it until they found a way to make it work.
It is said that Thomas Edison “failed” at his attempts to invent the light bulb over 10,000 times. When he was asked how he kept going, he simply believed that what he had in fact done was discover 10,000 ways NOT to invent the light bulb!
He never looked upon any of his attempts as failures. Instead, he saw them as a chance to learn and today you and I can sit by a lamp and read this article because of this man’s belief in success and his not believing in failure!
One thing you can do right now to begin moving yourself more in the direction that you want to go is begin looking ever action you take, every move you make as having no other possible outcome than being successful.
Did you get that? Think of EVERY action you take, every move you make, every phone call you make as a success, no matter what the outcome!
You will always succeed at producing some sort of result. It may not be exactly what you had in mind, but you will ALWAYS succeed at producing some sort of result.
Thomas Edison looked at every attempt to invent the light bulb as a success, even though he did not achieve what he had set out to accomplish. Think about it.
Had he considered his every attempt a failure, how many failures do you think he would have endured before he would have quit? My guess is that you’d be sitting in the dark right now if he had.
I believe that the only failure in life is the failure to take action. If you do nothing, nothing will happen. If you do something, anything at all, you will succeed in producing a result. In other words, you will create success in your life.
What if you created success in your life every single day? How would you feel?
What if you learned that success is yours to be had each and every day, and that with each little success you knew that you were one step closer to an even bigger success. Would you stick to it? Would you build on each day with more and more passion for what you do?
Would you soon be living the life of your dreams? You bet you would. And, you can, if you will simply give this some thought and then take action and begin looking not to your failures, but to every success you create each and every day of your life.
So from this point forward, set yourself on a new course. A course for success in all that you do. Look to your actions as successes, learn from every action you take and keep on taking action until you get to where you want to be in life.
The formula is simple, and the results will literally blow you away once you begin to apply this new thinking to your life.
Start with your web site. Is your web site a success? For some people, the fact that you have one at all is a success! Do you get the kind of traffic and sales that you really want from your web site?
What if you knew the most effective ways to bring more traffic to your web site? Would you jump at the chance to own this information so that you could apply it now and use this information for the rest of your life?
Today I know how to promote a web site to millions on a shoestring budget because I have worked at it for years. I was up late at night for thousands of nights. I tested this, and tried that. And I never looked at the things that didn’t work as failures. Instead, I learned from each strategy that I tried and today I can stand before you as one of the top Internet Marketing minds of our time!
Now if I told you that this information, when applied to your business, would help you double, triple, or even quadruple your profits in the next 12 months, how much would you invest to get your hands on it? I’ll bet you’d pay thousands of dollars for it! Yet you could get it for much less than that.
You know that you can learn from your mistakes, but did you know that you can also learn from other people’s mistakes? I’ve learned Internet marketing the hard way… I’ve been doing it since 1984. I made mistakes, I’ve lost money, and I learned from each and every one of my mistakes so that now I make a lot of money on the Internet.
I am one of the top marketers on the Internet. Clearly 100% of my clients make money on the Internet because of the mistakes I’ve made over the course of my career. I simply turned my mistakes into success and kept on going until I got to where I wanted to be.
You can do exactly the same thing that I have done, or you can take the shortcut and learn from my mistakes. You see, there are masters in every field. Most of them have books, tapes, or articles on what they did to get to where they are today. Get your hands on that material and learn from it. It is the shortest distance between you and your dreams.