# What does $x^{(i)}$ Mean or Denote

I know this is a simple question, but what does $x^{(i)}$ mean (where $x$ and $i$ are variables and $i$ isn't $\sqrt{-1}$) or what operation does it denote? I assume it's not a regular exponent. I saw it here: http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks/

• In this case, in particular, it's used to index the training set - see the paragraph right underneath 'Backpropagation Algorithm' where it spells out that the training set used is $\{(x^{(1)}, y^{(1)}), \ldots, (x^{(m)}, y^{(m)})\}$. – Steven Stadnicki Mar 27 '16 at 21:49

It looks like you have a sequence of vectors, each of which you want to call $x$. Since you want to reserve the subscript for indexing the components, we sometimes make the superscript index the vectors in the sequence. Usually we put this index in parentheses to help avoid confusion with exponentiation.