Even if theism is a failure, it's still superior to atheism

[polymath257]

"There is 'a' tallest tree" implies that there exists one tree that is the tallest tree, solely.

Nope. Existential quantification is different from uniqueness quantification.

There is a x, implies that x exists. In other words, at least one instance of x exists, This doesn't entail the uniqueness of x ,it may or may not be true. We're certain though that one example exists.

Besides, my example of a tallest tree was directed to polymath for a reason, he has serious background in math. If you didn't do much math above, take some time to parse this sentence to see that it doesn't entail uniqueness.

But you do need the observation that trees exist in order to deduce there is a largest one. You also need defined properties of height, for example (that it is linearly ordered) and that there are only finitely many trees (which cannot be known a priori).

For example, there is no tallest unicorn.

Also, there is a distinction mathematically between 'tallest' and 'maximally tall'. The first implies uniqueness while the latter does not.

There is also no maximally tall unicorn.

Again, I don't claim observation isn't needed at all, all arguments for God are based on empirical observation, after all. Can you give the mathematical equivalent of "tallest" here ? You mean a least upper bound ? Yes, a least upper bound is unique, it would be equivalent to the height of the tree in our hypothetical.

It is the height of a tallest tree that is unique, not the tree, so this not in conflict with the possibility that there may be many trees of this same length

There are other assumptions. For example, that the height is well defined for each tree. This is far from clear.

For example, can you really give the height of a tree to 20 decimal places? Is it even meaningful to do so?

There is also the difficulty of how to measure the height. Similar issues arise, for example, with the height of mountains (measure from sea level? or from center of the Earth?).

So it may well be that the tallest by one definition is not the tallest by another.

So, you are really claiming a counter-factual: if we measured the height of every tree, then there would be at least one of maximal height. In other words, if you made all of the necessary observations, the list of numbers given has a maximum.

This is not a statement about the existence of a tree, but a mathematical statement about the maximum of a set of finite numbers.