Infinite tetration and superroot of infinitesimal

[andydude]

Before proceeding further, I would like to be precise about what an "infinitesimal" number is.

• There exists no z such that \( 0 < z < a \) for all real \( 0 < a \)
  
• There exists dz such that \( 0 < dz < a \) for all real \( 0 < a \)
  

An infinitesimal is a number that satisfies the second property, is this correct?
How does this not form a contradiction with the first property?

Andrew Robbins