Savings and investing is a how to become wealthy. Photo: Flickr user Ken Teegardin.

Ask any honest financial planner how to become wealthy, and they'll tell you the simple act of saving money is far, far more important than picking the next hot stock.

So I was surprised when I came upon an article from The Billfold titled "You Don't Get Wealthy from Savings." The article was so wrought with pessimistic thinking and ridiculous assumptions that I couldn't help but debunk the most alarming.

Hopefully, by the end of the piece, you'll see that saving -- and some easy steps toward investing -- is key to becoming wealthy.

Problem No. 1: Saving 3% isn't how you become wealthy
I'll tackle the easiest problem first. The article said that if you have the median household income of $51,939, and you're saving 3% of that income pre-tax, starting at age 30 and following suit until age 65, you'll only have $192,686.34 by the time you reach retirement.

First of all, let's get one thing straight: If you want to prove that savings can't make you wealthy, you can't assume we're saving a measly 3% of our income to prove your point. All the example proves is that not saving will keep you from getting wealthy.

If we upped the family's savings to 10% and assumed an inflation-adjusted return of 6.86% -- which happens to be the true annualized return of the stock market since 1871 -- the family is now retiring with $745,000 in today's dollars.

Problem No. 2: Saving and investing for five years isn't how you become wealthy
The second problem with the article is a little more complex. Again, using the median family, the author ponders what would happen with a family that is able to sock away $10,000 per year, which comes out to a pretty awesome savings rate of 19% -- pre-tax.

What does the author find?

But $10K in a year is not wealthy. Even $50K in five years is not wealthy. That is the type of savings that pays for one year of your child's college education.

Who in the world thinks they can get wealthy from just five years of savings? That's ridiculous. If, as in the previous example, we were talking about someone investing over a 35-year time horizon, the results would be much different. The final balance in your portfolio -- again, using the average inflation-adjusted returns of the stock market -- would be $1.4 million in today's dollars.

If we take Social Security into account, this couple would even be able to retire early.

Now, that figure might actually be a little lower, because you'd likely want to diversify toward less risky investments as you aged, but you get my point. You can't claim that saving and investing in a total-market ETF doesn't create wealth if you're only using a five-year time frame.

Problem No. 3: What's our definition of wealth?
But the most insidious problem with this article is that it doesn't define "wealth." All we're told is that $50,000 isn't wealthy, nor is $193,000 in a retirement account at age 65. Of course, you wouldn't have a hard time getting most people to agree with those two premises, but that's not the point.

Without some kind of threshold, anyone could say that "wealth" means being a multimillionaire -- or maybe even a billionaire. If that's the line being pushed in the article, it's a sad statement of where our priorities are.

I've often said that finding your "Enough" is what matters most, and fellow Fool Morgan Housel has shown how easy it can be to feel wealthy if you adjust your perspective and understand that the only true measure of wealth is freedom of time -- not your net worth.

I guess that leaves us with two simple questions: What is your definition of wealth, and is obtaining it important to you?