Got hired as adjunct this semester and was given Real Analysis to lecture to which I was more than excited to do so.

However recently when I tried to explain how the set [0,1] contains and infinite amount of real numbers I was immediately met with skepticism by a student.

He proceeded to press me on the matter and since I was new I became visibly anxious, slurring my words which was further intensified when I deduced that the set was not just infinite, but uncountably infinite to which another student smirked and pressed me on what it means for a set to be countable /uncountable

At this point I was visibly uncomfortable as it is a very bad sign to be doubted not just once but in a consecutive matter to the entire class.

The final straw was when I, using the same reasoning arrived at (0,1) having the same cardinality as the entirely of R to which a different student proceeded to walk out of the classroom.

By the end, I was sweating bullets and I am now dreading coming back to lecture next class.

What am I doing wrong? I know the topics in real analysis are unintuitive but it seems like most of the class thinks im bullshitting I even notice the same students quietly laugh everytime i mentioned the word countable now.

Is it normal to be pressed this much as a first time teacher ? if my students are now skeptical is there anything I can do to win their trust back?

If the anxiety Is preventing me from effectively lecturing will I have to resign?

I am absolutely terrified as I have to touch on cauchy sequences and equivalence classes very soon and I do not even want to know how they will react

I think I will have to talk to the chair of the department for any options at this point