How does one distinguish between true knowledge (Vidya) and ignorance (Avidya), and what are the consequences of each?

Chapter 37 provides a clear distinction between these two concepts. True knowledge, or Vidya, is defined as that which has 'Shreyas' (the ultimate good) as its subject. It is the science of the oneness of Brahman and the Self, and it is the means to ultimate liberation. The consequence of Vidya is the cessation of birth and death. Conversely, ignorance, or Avidya, is that which has only 'Preyas' (the pleasant) as its subject. It is the root cause of perceiving manifoldness and duality. The text warns that anyone holding even a slight view of difference, a product of Avidya, will fall into the sufferings of birth and death.