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Use "indiscreetness" in a sentence
"As much as he hated to say anything against her, he would not trust her with confidential information because of her “indiscreetness.”"
"Mrs. Burton, who was staying at Brighton, wrote to Miss Georgiana Stisted a most kind, sympathetic and beautiful letter — a letter, however, which reveals her indiscreetness more clearly, perhaps, than any other that we have seen."
"But his indiscreetness and pure stupidity in babbling to Pearlstein as he did is not a story unless SI decides it a story."