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hi, my question is related to a proof involves bland rule for avoiding the degeneracy. Initially I emphasized some sentences which have importance in attachment/file with yellow color.
At the beginning, it says xs is entering variable and when it enters objective value does not change( because all dictionaries are degenerate) which means xs will become basis and have 0 value. Afterwards it says xs=y ( y be arbitrary number), and is establishing the equation 3.10 which suits every value of y. Here my question is : Saying that xs=y ( y is arbitrary) is wisely/reasonable although it says that xs is designated to be a entering variable at first which means when it enters objective value does not change (which means xs will become basis and have 0 value)??? Because later it establishes the equation 3.10 and says this equation should equal to zero for all y. But I think xs should only take 0 value because it is a entering variable at the beginning and when xs become basis it has 0 value because of the fact that objective value should not change??
I hope my question is explicit for you
At the beginning, it says xs is entering variable and when it enters objective value does not change( because all dictionaries are degenerate) which means xs will become basis and have 0 value. Afterwards it says xs=y ( y be arbitrary number), and is establishing the equation 3.10 which suits every value of y. Here my question is : Saying that xs=y ( y is arbitrary) is wisely/reasonable although it says that xs is designated to be a entering variable at first which means when it enters objective value does not change (which means xs will become basis and have 0 value)??? Because later it establishes the equation 3.10 and says this equation should equal to zero for all y. But I think xs should only take 0 value because it is a entering variable at the beginning and when xs become basis it has 0 value because of the fact that objective value should not change??
I hope my question is explicit for you
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