Good numerical analysts and mathematicians do delta epsilon proofs to figure out what a mathematically undefined quantity should be in specific cases to provide continuity, then redefine the definition in a specific instance. For example a correlation between two sets with zero variance, isn't defined, division by zero, but it's pretty obvious that a value of 1.0 or perfect correlation makes the most sense when doing hierarchical clustering.
A more general issue is that using fold changes is likely to amplify noise.
