Maximum number of images to train a convolutional neural network
Theoretically speaking, there is no limit on how many data points you can use to train any neural network. This is true because neural networks that can be trained incrementally and do not need to "see" the entire dataset.

Obviously, it helps if your machine is able to store at least a single image and the network in memory.

To train on a large number of images, you will likely need to use batches. This means that each iteration happens on a subset of your data, which can be as small as a single image.