Proof that an uncountable subset is from an uncountable parent set

[bitter kettle]

I don't really know how to start this, I'm not super comfortable with starting informal proofs.

[gloomy scroll]

Assume X is countable
Make a set Z that is the difference between X and Y
X is countable, meaning you can mark each element with a unique integer
Mark each element of X with a distinct integer
Remove all elements of X that is in Z
You would have Y as X-Y = Z so X-Z = Y
Every element of that set is marked with a unique integer, therefore Y must be countable
If X is countable, Y is countable

[sage wigeon]

That sounds like contrapositive not contradiction

[gloomy scroll]

It is. I don’t think the question is asking specifically for a contradiction tho, it just suggests it

[bitter kettle]

thanks! sorry i just got around to looking at this two days later