Socialism

I know at one time there were zero bikes, now there are more than zero, and I suspect more will be created...

Correct but, there cannot always be more bikes... At some point there may not be demand for more, or materials run out or become too expensive... Taken to the extreme, you cannot produce more bikes forever

For discussion, perhaps it would be easier to reduce the complexity. In a capitalist system, if I own a fruit tree in an ideal climate then not only can it be duplicated, but either it will produce value by itself, or I will by picking its fruit.

Again, globally we may produce x billion tons of fruit this year.... Maybe a few million more next year... Can we always produce more fruit (more as in a greater number than last year) forever?

There are only two ways of producing "value". You either extract resources from the planet or you use labor to enhance those resources. The value is in the problems solved by the finished product.

Capitalism requires that capital is invested in the manner which produces the most profit. Thus infinite growth.

There is not an infinite amount of resources or labor. The fruit tree extracts nutrients from the soil and requires water to be added.