Used to highlight a period in the past, usually a few decades ago or when speaking of one's younger years. In my day, we respected our elders much more.
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Nostalgic Tone
Often implies a longing for the past or a belief that things were better or purer then. People really knew how to dress in my day.
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Generational Contrast
Used to contrast past generations with the present, sometimes leading to intergenerational discussions. In my day, we didn't have smartphones to distract us.