Limits

Limits are everywhere. Speed limits. Credit limits. Time limits. Character limits. And, of course, mathematical limits. What are the reasons for these limits? Are you limiting yourself?

What's the limiting case?

Mathematically speaking, a limit is written as

.

We read it as "the limit of f of x as x approaches c."

It's often a useful exercise to consider the extremes of a limit—what happens if the limit approaches 0? What if it approaches infinity? For example, the simple function

is graphed below. We can see that as x increases, the function tends toward 0. As x decreases, the function tends toward infinity.

Consider the ideal gas law:

where n and R are essentially constants (n is the amount of gas; we'll assume it isn't going to change), P is pressure, V is the volume, and T is the temperature. We'll also assume that pressure is constant, since we're likely on the surface of Earth.

We can then say that the volume is proportional to temperature, or

So what happens if T increases? V also increases. This makes sense, since we know that as temperature increases a gas will expand (or increase in volume.)

Where am I going with all this?

I often like to test my own limiting cases. I always ask myself, what's the worst that could happen? Or, what happens if x goes to 0? I don't need to know the details of every situation or plot every single data point along the way. I just need to know what the extremes are.

Most often, the worst-case scenario is never that bad. What's the worst that could happen if I submit my story to the publisher? They say "no." Big deal. So just do it. Or, conversely, what's the best thing that could happen if I submit my story? I end up getting published and fulfilling my dream. So why not try?

What's your limit?

It's a good thing we humans aren't mathematical equations, having limits to our success or brilliance. As Ronald Reagan said,

So what are your limits? What's holding you back? I propose that fear is the most limiting factor in our lives. But fear of failure? Or fear of success?

Once you know your limits, you can defy mathematical laws and go beyond them, achieving success and abundance greater than you thought possible. You just have to be willing to test yourself and believe in your own power to make your dreams a reality. It may seem formidable, even impossible, but as we say in particle physics, forbidden transitions are highly discouraged.

There are no great limits to growth because there are no limits to human intelligence, imagination, and wonder.

"The only limits you have are the limits you believe."

~ Wayne Dyer

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