Why can't the XOR linear inseparability problem be solved with one perceptron - like this? Consider a perceptron where $w_0=1$ and $w_1=1$:

Now, say we use an activation function
$f(x)=1,~for~x=1$$~~~~~~~~~~~~~0, otherwise$
The output is then summarised as:
$x_0~~~~~x_1~~~~~w_0*x_0 + w_1*x1~~~~~f(.)$
$0~~~~~~~0~~~~~~~~~~~~~~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~0$
$0~~~~~~~1~~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~~~~~~~~~~~~1$
$1~~~~~~~0~~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~~~~~~~~~~~~1$
$1~~~~~~~1~~~~~~~~~~~~~~2~~~~~~~~~~~~~~~~~~~~~~~~~~~~0$
Someone tell Rosenblatt I solved his problem ...
...or have I?
Is there something wrong with the way I've defined the activation function?
Your function


  0,otherwise 1


is not a linear combination of the inputs.

From the definition of single layer perceptronL


  A single layer perceptron (SLP) is a feed-forward network based on a threshold transfer function


Your function has two thresholds:  one for &lt; 1 another for >1