>>8
You are wrong.
If you insist on considering only 'real' machines, having a finite amount of memory, obviously your halting problem solver have to be a 'real' algorithm as well. But, as you said yourself, to determine if some algorithm running on a storage limited to n bits goes into infinite loop you should have 2**n bits of storage. Thus any reasoning going along the lines of "we can't really run an algorithm requiring more than N bits of storage (for some very large yet finite N), so all algorithms we CAN run are decidable" is fallacious: the decidability is made impossible by the very same assumption.
You can witness the same fallacy in the neighbouring thread, where some unsuccessful troll or a genuine idiot insists that since all practical regexes are bounded in size, one can describe them using regex - forgetting, that this regex itself is guaranteed to exceed any given "maximum size".
Also, it's interesting to note that considering only "practical" algorithms is actually ane and fruitful and it's what complexity theory is about, however it looks like halting problem corresponds to P!=NP there.