No I meant continuous with this definition "A continuous data set is a quantitative data set representing a scale of measurement that can consist of numbers other than whole numbers, like decimals and fractions. Continuous data sets would consist of values like height, weight, length, temperature, and other measurements like that. They're things that can be measured in fractions and decimals. Usually a tool, like a ruler, measuring tape, scale, or thermometer, is required to produce the values in a continuous data set." But yes the superset is an uncountable which would be the more encompassing definition but more difficult to understand.

As far as a method it's a el5, thus a master level proof would not be appropriate. Regardless the method I explained is the baseline for proving that a infinite is not countable via the proof of contradiction.

So there are infinite many infinity but let's talk about the two most common one, countable and continuous.

Countable is any thing one can count, think of the number 0,1,2,3,4...78810836689017,.... This will go on forever thus infinite, but in a infinite amount of time one could count all of the numbers (this is not possible for human because we have finite time).

Continuous think of decimal pick two decimal call the larger one B and the sampler one A, then pick a decimal C; where C is in-between A and B, then repeat (C will now be B and one will pick another C) This will go one forever and you can always find another decimals that we didn't account for. One can't "count" all of the decimals because you can always pick another decimals between A and B.

Follow up point, the reason the first infinite is countable is because you can create a function to get to all of the number by adding one (in the example above), but you can make a function to get all of the decimals.

(Not quite el5 because of the math I know, but it's the best I know how to do)