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The answer is simple......there is no such thing a wave with and infinite wave length... it makes no sence... and wave with and infinte wave length is a line... there can be no wave.... so lets work on something less than infinite... a wave lenght of 500 trillion light years to the power of 3000... now although that is a very long wave is is not infinite in fact it is still infinitely removed from that length...
When dealing with finite inputs you can not get a result producing an infinity... you can not double finite to reach infinity nor can you halve infinity to come to a finite...
There must always remain a wave if the sums say otherwise they need adjustment.
alex
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