Without regard to; not taking something into consideration; regardless of.
From 'ir-' (not) plus 'respective' (relating back to). It's a fairly modern coinage combining prefix and existing word to create the meaning 'not showing respect to/ignoring.'
Grammarians argue whether 'irrespective' is even a real word—it's often considered redundant with 'regardless'—but it's persisted because people like how emphatic it sounds!
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