Why stop there? They're just as real as any number.

Just say you recently came into some inheritance and that you are looking into investment opportunities. Then they will expect you to be out of your element, so you won't need to try to pretend you're someone you're not. If they ask about the inheritance, say your grandfather made a fortune selling lumber or something boring like that.

A vector space is a collection of vectors in which you can scale vectors and add vectors together such that the scaling and addition operations satisfy some nice relationships. The 2D and 3D vectors that we are used to are common examples. A less common example is polynomials. It's hard to think of a polynomial as having a direction and a magnitude, but it's easy to think of polynomials as elements of the vector space of polynomials.

sets a dangerous precedent where the government knows better than the markets

Wtf. You could say this about literally any law. Outlawing murder-for-hire sets a dangerous precedent where the government knows better than the markets. Making people pay income tax sets a dangerous precedent where the government knows better than the markets. Speed limits set a dangerous precedent where the government knows better than the markets. What a terrible argument.

It's funny you say the philosophy is simple when strategic voting requires multiple layers of analysis and voting for bubblegum ice cream just amounts to what feels good. You can't bring yourself to accept the reality of the situation, so you pretend like the problem is easy to solve if you just ignore it. That's truly simple minded. Pathetic projection on your part.

Doesn't matter where the track leads if the trolley can't get to it. It could lead to rainbows and sunshine, but that isn't where the trolley is headed because there is no possibility that someone other than Trump or Biden is elected president. A few cry babies voting third party won't get some third person elected. A vote for the third track is a vote for a track that will not be ridden.

It's supposed to be E^2 = (mc^2 )^2 + AI^2 , which implies that AI = pc, because AI is the momentum that will carry us into the future. These rookies clearly just took the square root using freshman's dream.

I like this one

It depends. If the variable names are arbitrary, then a map is best. If the variable names are just x_1, x_2, x_3, ..., x_n, then a list or dynamic array would be more natural. If n is constant, then a vector or static array is even better.

I don't recall any socialized courier or food delivery services.

This is just a continuous extension of the discrete case, which is usually proven in an advanced calculus course. It says that given any finite sequence of non-negative real numbers x,

lim_n(Sum_i(x_i^n ))^(1/n)=max_i(x_i).

The proof in this case is simple. Indeed, we know that the limit is always greater than or equal to the max since each term in the sequence is greater or equal to the max. Thus, we only need an upper bound for each term in the sequence that converges to the max as well, and the proof will be completed via the squeeze theorem (sandwich theorem).

Set M=max_i(x_i) and k=dim(x). Since we know that each x_i is less than M, we have that the term in the limit is always less than (kM^n )^(1/n). The limit of this upper bound is easy to compute since if it exists (which it does by bounded monotonicity), then the limit must be equal to the limit of k^(1/n)M. This new limit is clearly M, since the limit of k^(1/n) is equal to 1. Since we have found an upper bound that converges to max_i(x_i), we have completed the proof.

Can you extend this proof to the continuous case?

For fun, prove the related theorem:

lim_n(Sum_i(x_i^(-n) ))^(-1/n)=min_i(x_i).

2 may be the only even prime - that is it's the only prime divisible by 2 - but 3 is the only prime divisible by 3 and 5 is the only prime divisible by 5, so I fail to see how this is unique.