**Formula for Success: Applying Math to Achieve Your Goals**

*How Mathematical Induction Change My Life*

When I was an undergraduate, I learned about proof by induction for the first time in Discrete mathematics class. It was inspiring, and it helped me change how I approach success in life.

# What is Proof by Induction?

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

— Concrete Mathematics, page 3 margins.

Proof by induction is a mathematical method to justify statements. It consists of just two steps.

**Step 1:**Is the statement true for the first step?**Step 2:**If any step is true, is the following step true?

If the answer was yes for both steps, the statement is then true by this method.

# Dominos effect and success

One of the best examples for proof by induction is the dominos effect.

- Step 1: Knocking over the first domino.
- Step 2: When domino number N falls, will it knock domino N+1?

This is how proof by induction inspired me. It told me that If I can have a small success today, and a small success tomorrow, then most probably I can have more success with every coming day!

# Success Builds on more Success

While everyone tries to learn from failure, I believe learning from success is easier, and more *fun*. Success increases self-esteem, self-discipline, consistency, and is a sign that we can succeed. While failure may drive you to believe that you will never do it.

That’s why I learned to plan for small successes to bring on more success. Let’s say I want to stop eating sugar. Can I challenge myself for just today to not eat any sugar? Yes! Can I apply the same challenge for tomorrow too? Yes. What about after tomorrow? Yes. So If I can do it today, tomorrow, and after tomorrow, I know I can do it. Will I fail sometimes? Yes, no doubt! But if I can succeed most days, I can still succeed.

Mathematical Induction inspired me with many success tips.

# 1. Small Goals

To learn from success, you need to plan for “training success”. We tend to think in an “all or none” mentality. You plan for a big goal and wait for a big success, so when you fail you get disappointed and have that feeling, we all know too well, that I will never do it.

Instead, I learned to break big goals, into small training “stepping stones” goals. So whenever you are done with one, you are encouraged that you can do more.

**Example**: You want to publish a book in 2020. This is a big goal, that you may fail in achieving. You start to write a lot to finish that book, then suddenly get too busy, start procrastinating and you just fail to succeed. You can instead break this goal into: “I want to write for 20 minutes every day” and now you have a little goal that you can achieve every day!

Set small goals along the way and don’t be overwhelmed by the process.

Kara Goucher

# 2. Only Think About Today

After planning for your mini-goals, just challenge yourself to do it today. Let’s say you want to be strong, so you set a mini-goal to exercise daily for 20 minutes. With each day you need to only think about today, challenge yourself to finish those 20 minutes and that’s it. Try not to discourage yourself by thinking about how consistent you need to be to reach your end goal.

Change your life today. Don’t gamble on the future, act now, without delay.

Simone de Beauvoir

# 3. When You Fail: Ignore It

Unless you are failing every day, learn to ignore random failures. If someone sleeps daily at 8 pm and slept once or twice at 3 am, will he call himself a night owl? Impossible! Same to you, if you could stop sugar today, and on most days, but you couldn’t do it once in a while, you should ignore those missed days without thinking you can never succeed. Most people decide to fail, after the first slip up.

If you fell down yesterday, stand up today.

H. G. Wells

# 4.Trust Mathematical Induction

Can I have 100k followers on my Twitter account? 100k is a big number, so let’s apply mathematical induction to it. Can I get 10 followers today? Yes, I will just go and follow multiple people that I find interesting, some of them will follow me back, and I could be followed by 50, not just 10! Great, can I do this tomorrow too? Yes! then I can get the 100 k followers eventually!

# 5. Just Start

I followed Twitter users as a way to get followers. I assumed that this way can get me 50 followers a day, so if I can get 50 followers a day, eventually I will get the 100k, right? Yeah but this would take around 6 years! Ironically, It will take even longer to reach 100k, if you don’t start!

The secret to getting ahead is getting started.

Mark Twain

# 6. Grow with Time

Another piece of advice is that you can enhance by using more tools for success step-by-step. So when you know you can get 50 followers a day, work on getting 100 instead, then 150, then 200, and so on. You will learn and apply what you learn as you grow.

# A Final Note

I have a tip for teachers, caregivers, and anyone trying to help others to succeed; give them small challenging goals that they can succeed in. Everything will be easier after that, as they will have a stronger belief in themselves and then they become more capable of doing more effort to succeed.