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I recognize this is a useful intuition for people beginning math (especially applied, especially stats), but the problem is that the actual formalisms disagree: discrete is trivially continuous. Look no further than https://en.wikipedia.org/wiki/Discrete_space : we can give anything a topology and make it continuous. And this isn't actually that removed from stats: More advanced stats, e.g. working with arbitrary probability measures. uses highly related formalisms.
I don't want to derail, and especially don't want to get into a sub-field war, but at least calling out the various uses of the terminology and how they conflict would I think be useful. <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Sonarpulse|Sonarpulse]] ([[User talk:Sonarpulse#top|talk]] • [[Special:Contributions/Sonarpulse|contribs]]) 05:49, 12 January 2020 (UTC)</small> <!--Autosigned by SineBot-->
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