What is the activation function for?

Question

Neural networks

Started studying machine learning. I tried to figure out how the perceptron works, and I ran into the fact that I don’t know what the activation function is for and what it should do.
With the rest of its parts (input data, weights, neuron), how they work and what they are for, I have already figured out. Please explain what the activation function is for, if possible with a specific example.

Answer 1

For non-linearity, otherwise everything can be reduced to some simpler formula than 100500 coefficients.

Answer 2

The activation function cannot be explained in isolation from the neuron. The main requirements for it are continuity and monotonicity over the entire domain of definition. Either the logistic sigmoid or the hyperbolic tangent is taken as such a function. They are saturated at the borders. That is, the infinite growth of the argument does not lead to the growth of the function.
The function is related to Kolmogorov Arnold's theorem.