Unusual notation for integer, rational and real numbers (A. J. Moakes M.A., The Core of Mathematics)

Question

I am reading currently an old book: A. J. Moakes M.A., The Core of Mathematics, An introduction to 'modern' mathematics (1964). The author uses some unusual (at least to me) notation for integer, rational and real numbers alike:

Are there other authors that use such a notation? Is just an 'anomaly' of the author's book?

Thanks a lot.

Answer 1

page 25 in the third edition of baby Rudin. Earlier he says properties of the integers will be assumed; from what I can see, he uses integers mostly as an indexing set for sequences or series, so positive integers. I'll try to find a later page that uses $J$