Um, no. Nothing in the economy is zero sum. Wealth is constantly being created and transferred.

Created and transferred are two different things. Created means new wealth is generated through increased efficiency or innovation. The pie gets bigger. Transferred means one player loses and the other gains (the definition of zero zum). The pie stays the same, only the relative size of each slice changes.

Secondly, increasing competition increases pressure to become more efficient and/or innovative, which in turn drives market growth. The whole idea of helping and soliciting help in business is an act of innovation.

You argue that increased efficiency is a kind of innovation. Your argument is that increased competition leads to increased efficiency, and by increasing efficiency in a market more resources are freed for other markets and the pie gets bigger.

I may agree with you here, but you'll have to provide examples.

*
Increasing the quantity of entrepreneurs by default increases the quality, because it increases the pressure to compete, and therefore leads to the very innovation you feel is the real solution*

Can you provide concrete examples?

Several points:
I can agree with your argument on a theoretical level but its still a leap to make the connection between increased quantity leading to innovation without evidence or examples.

1) One instance in which your argument could be true:
If there are greater efficiencies discovered in one industry (for example, a new gizmo that doesn't require as many restaurant cooks), leading to less labor costs and subsequently lower cost of food, leading to increased money in consumer's pockets with which they could spend in other industries.

But who discovered that efficiency? It could be made by a separate party and have no connection to the increase of competitors. It is a leap to draw the correlation between increased competitors and innovation.

2) One instance where it may not be true: An industry where there are little or no efficiencies to be captured.

Lets say there are 10,000 software design firms competing with one another and they make their profit from software consulting projects. If they all make a profit of $1,000,000 / year and you add another 10,000 competitors, all providing the same service, two things will happen for sure:
1) some of the new competitors will gain entry to the market, leading to lower profit for everyone else.
2) some competitors will fail.

It is possible that the innovations are simply not there to be found by the new entrants, even with their newfound startup wisdom. Innovation is not a matter of strictly effort. For example, I recently came back from a trip to Southeast Asia where I traveled for 3 months across many of the developing countries and witnessed the effects of increased competition there among the street hawkers.

In the street-hawking industry there simply aren't many innovations to be discovered. Adding more entrepreneurs to the mix wouldn't lead to innovation, but rather a race to the bottom. Profits across the board would decrease and consumers would benefit.

Also, a point about quality: increased quality does not necessarily lead to a greater pie. We may lead richer lives from 10% more delicious food but the wealth pie stays the same. (although that is valuable as well).