Sorry CJ but I don't buy your maths. Methinks thou does't confuse a moving and static frame of reference (or something).
I remain convinced that a turbine aircraft can fly faster than its exhaust gas velocity and can see no reason why not, once you abandon the intuitive feeling that the exhaust gas has some effect after it has left the engine. I am happy to be proved wrong and I was rather hoping a mechanical engineer or physicist might come to my rescue (where are they when you need one...??) But the arguments presented on this thread so far do not convince me I am wrong. As Poirot would say: "Ze truth will reveal itself"
As a matter of interest, I had a quick squiz at the jet turbine data sheets and amongst the heaps of technical data, I could find no mention of exhaust gas velocity. Surely if it were a limiting factor in the engines use, it would be specifed?
The other point to note is that high bypass turbofans have low speed (subsonic) gas flows (albeit at a high mass transfer) and yet a high bypass turbofan can fly at M0.85 (easily) and perhaps more - as far as I can see, the only limit to higher speeds is if there is enough thrust to overcome the steeply rising drag.
I am away from the net for a day or two, so I will not be participating in this interesting discussion for a while.