Boundness of a Neural Network Weights Using the Notion of a Limit of a Sequence

feed forward neural network with backpropagation learning algorithm is considered as a black box learning classifier since there is no certain interpretation or anticipation of the behavior of a neural network weights. The weights of a neural network are considered as the learning tool of the classifier, and the learning task is performed by the repetition modification of those weights. This modification is performed using the delta rule which is mainly used in the gradient descent technique. In this article a proof is provided that helps to understand and explain the behavior of the weights in a feed forward neural network with backpropagation learning algorithm. Also, it illustrates why a feed forward neural network is not always guaranteed to converge in a global minimum. Moreover, the proof shows that the weights in the neural network are upper bounded (i.e. they do not approach infinity).