“Chuck Norris' credit cards have no limit. Last weekend, he maxed them out.”

Credit cards have limits—a maximum spending amount beyond which the card will be declined. This limit is set by the issuing bank based on creditworthiness, income, and payment history. Wealthy individuals might have higher limits, sometimes in the hundreds of thousands of dollars. But even unlimited-seeming credit cards have practical limits; there's always a ceiling beyond which additional charges are impossible. The limit represents the bank's assessment of acceptable risk.
Then this fact asserts that Chuck Norris's credit cards have no limit. And then, crucially, he maxed them out. If there's no limit, how can he max out? The paradox is the punchline. He possessed something theoretically unlimited, and through sheer capability and desire, he exhausted it completely. The implication is that his spending capacity exceeds infinity. He spent enough in one weekend that even unlimited resources became finite.
What makes this work is the logical paradox packaged as casual braggadocio. The fact doesn't say he spent a lot; it says he spent beyond what should be physically possible. Credit card companies probably called him in confusion, unable to process that unlimited accounts could be maxed. He's achieved something that contradicts the basic structure of financial products: he's exceeded a limit that shouldn't exist.
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