In keras documentation, input tensor for dense layer takes the input as:
Input shape
nD tensor with shape:
(batch_size, ..., input_dim). The most common situation would be a 2D input with shape(batch_size, input_dim).
To my understanding, batch size in input tensor is the amount of examples you give for training or predicting.
For the batch_size in model.fit, 
batch_size: Integer or
None. Number of samples per gradient update. If unspecified,batch_sizewill default to 32.
So are the 2 batch size doing the same thing, reducing the input data so as to prevent memory from filling up completely?
Also, I understand that the batch_size in input shape is optional, as keras puts a None if not specified. Is specifying batch_size necessary in model.fit?
 
    