There is another approach, which I believe makes much more sense, one based less on pie-in-the-sky and more on what we can realistically plan for. For this plan, the starting point is how much we spend each year or plan to spend. This is something we all have direct control over. It defines at the outset what is the essential purpose of all our assets, which is primarily to meet our living needs and places our investment approach in this context.
Once we have established our annual living expenses, we need to calculate our total "passive income" (PI). Primarily this will be our wage or pension income, it should also include any income that results from passive investments or businesses, that involve no additional action on your own part. Trading profits or capital gains do not count here, but income from your investments would, so long as they can be regarded as recurring income.
The health of your finances can then be determined by comparing your annual spending plan with your PI. If your income matches or exceeds your spending then congratulations! You are wealthy by my definition. Other people may have more assets than you do, but they may not be as wealthy if they are not living within their expenses. As regards your investments, you have gained a good deal of freedom. In order to further increase your wealth you still need to carefully measure your risk against your return, and manage your positions to avoid losses, but at the margin you can clearly embrace more risk than otherwise, depending on your willingness to do so.
If your PI is below your annual spending then don't worry, I strongly believe that the great majority are capable of becoming wealthy as defined above, within a few years, if they choose to take appropriate action. The benefit of this approach is that it shows clearly where you currently stand, and automatically it will suggest some things you can do to move closer to becoming wealthy. In the mean time you can still invest but you may need to take care about how much risk is appropriate.