{'fraction_non_alphanumeric': 0.017045454545454544, 'fraction_numerical': 0.0, 'mean_word_length': 4.568421052631579, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Large families of almost disjoint large subsets of N

In the paper we study the question of possible cardinality of a family of almost disjoint subsets of positive integers each being large with respect to a given criterion. For example, it is shown that there are continuum many almost disjoint subsets of N where each set is large in both the sense of (R)-density and in the sense of the upper weighted density. On the other hand, when considering sets with positive lower weighted density, the result is completely different.