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**How do we know the speed of light "exists"?**

If we "know" that it can't be reached, how do we know it exists? Like I am looking at this from a math view.

So okay, "infinity" is not a number, it is a concept. It took me about a year of convincing to settle it down.

So is the speed of light the same thing? Not a number, but a concept? How do know this certain number 3 * 10^8 is not possible? Because I am just loooking at this as a number and the book tells me this is impossible.