Perhaps, but they do still need to know who’s going to be absent even if they’re going to approve it either way

It’s only true of badly designed bridges, these days. Modern engineering tools can calculate the resonant frequencies, and they make certain that those are far away from the frequencies which humans or wind can create

Israel and trump appear to be claiming to have defeated the Iranian air defense, and achieve air supremacy over the Iranian capital.

If that’s true then Iran is in deep trouble, and inviting them to surrender wouldn’t be unreasonable. I very much doubt that it is true, but that’s what they seem to believe

It’s far harder to achieve mass manipulation of the ballot when it’s all being handled by a lot of human hands. If it’s managed by computers, then by finding a bug or other vulnerability in the software or database you could alter the whole election.

Meanwhile, to manipulate a paper ballot & hand-counted election in the same way you’d need the cooperation of a huge number of people, and you’d need them all to keep their mouths shut. That’s far more difficult than defeating a computerised system

Honestly I think it’s misleading to describe it as being “defined” as 1, precisely because it makes it sounds like someone was trying to squeeze the definition into a convenient shape.

I say, rather, that it naturally turns out to be that way because of the nature of the sequence. You can’t really choose anything else

X^0 and 0! aren’t actually special cases though, you can reach them logically from things which are obvious.

For X^0: you can get from X^(n) to X^(n-1) by dividing by X. That works for all n, so we can say for example that 2³ is 2⁴/2, which is 16/2 which is 8. Similarly, 2¹/2 is 2⁰, but it’s also obviously 1.

The argument for 0! is basically the same. 3! is 1x2x3, and to go to 2! you divide it by 3. You can go from 1! to 0! by dividing 1 by 1.

In both cases the only thing which is special about 1 is that any number divided by itself is 1, just like any number subtracted from itself is 0