# How to prove that text is linearly separable?

I sentiment analisys task, for this I used SVM with an rbf kernel and a linear one. The results for the linear kernel were better than the rbf, from this I know that text is linearly separable, but how can I provide a formal proof of this?.

You can't formally prove this, unless you happen to be able to fit a hard margin SVM on your data (unlikely). However, intuitively, text representations are high dimensional (bag of words, n-grams, ...). The higher the dimensionality, the easier it is to linearly separate data, as the VC dimension of a linear classifier in $d$ dimensions is $d+1$ (e.g. see these slides). The VC dimension is the largest amount of points that a classifier can shatter (separate).