e sample drawn will contain two reasonably large disjoint subsamples <span class="math inline">\(\mathcal{S}_+\)</span> and <span class="math inline">\(\mathcal{S}_-\)</span> that are far apart (i.e., with total variation distance <span class="math inline">\(d_{\text{TV}}(F_{\mathcal{S}_+},F_{\mathcal{S}_-}) =1\)</span>).</p>
<details><summary><b>I like maths. Show me a proof.</b>
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Fantastic. Observe that <span class="math inline">\(K_+\)</span> and <span class="math inline">\(K_-\)</span>, define