Recent comments in /f/explainlikeimfive

sterlingphoenix t1_iub0v30 wrote

What it also does is provide balance while standing and -- more importantly -- running. Humans are the best endurance runners in the animal kingdom and out posteriors are largely responsible for that. We could chase down prey until it got too tired to run away and then club it.

Clearly this was a bigger advantage than disadvantage. Evolution is not directed.

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m4nu3lf t1_iub02h4 wrote

Economic growth is measured in GDP growth. GDP is roughly speaking the monetary value of the goods and services a country producers. The monetary value of a good or service roughly correlates with how much people want that thing. Hence it's almost tautological (trivially true) that people want economic growth.

Indeed economic growth isn't required. It usually just happens as people produce the goods and services they or others want more efficiently or with more resources.

Can growth go on indefinitely? Basically yes. Nowadays a lot of things of value are just information (think about a computer game). We can produce a lot of information. Also, even if there were hard limits to what you could produce, you can have infinite growth by asymptotically getting closer to what is the theoretical maximum without hitting it, although growth will be slower and slower.

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breckenridgeback t1_iuaziy4 wrote

Reply to comment by Chromotron in Eli5: Infinity ♾️ by [deleted]

> Conversely, there are uncountable "discrete" ordered sets where nothing is between a number and its two neighbours.

That's not true, and it's (relatively) easy to prove.

Consider a set S that is a subset of the reals, with the property that for each s in S there exist two numbers u and l (for "upper" and "lower") such that u < s < l and there are no numbers x for which u < x < s or s < x < l. In other words, u is the "next biggest" number and l is the "next smallest" (this formalizes the idea you've stated informally).

For each s in S, consider the radius R = min(d(s,u), d(s, l)) (of course, R, u, and l all depend on s, but reddit markdown means I'm gonna skip the subscripts). This radius is basically just the "minimum spacing" around s. Such an R exists for each s, and is strictly positive. Since R is strictly positive, so is R/2. And since the rationals are dense in the reals, we can find two rational numbers a and b (again, also dependent on s) such that s - R/2 < a < s < b < s + R/2. In other words, we can find an interval of rational numbers (a,b) that does not overlap the corresponding interval for any other s in S.

Now, consider the function f: S -> (Q x Q) that takes each element s in S and maps it onto the ordered pair of the interval generated by the process in the previous paragraph. This function is clearly injective, since none of the intervals (a,b) overlap (so they certainly cannot be the same), but the set (Q x Q) is a Cartesian product of countable sets and therefore countable. Since we have an injection from S to a countable set, S is itself (at most) countable.

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muthian t1_iuawfc1 wrote

Note that firewalls, both the classic and digital versions, are designed to delay for a period of time, not completely stop the danger on the other side. Given enough time without any changes to the firewall, it can be breached (either through intense fire or novel digital attack it's software hasn't been made aware of).

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explainlikeimfive-ModTeam t1_iuavwp9 wrote

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snoias t1_iuav9h0 wrote

Reply to comment by superbyrd22000 in Eli5: Infinity ♾️ by [deleted]

> So there are infinite many infinity but let's talk about the two most common one, countable and continuous.

I think you mean "uncountable", not "continuous". Or possibly "the continuum", which is sometimes used as a fancy word for the real numbers.

> Countable is any thing one can count, think of the number 0,1,2,3,4...78810836689017,.... This will go on forever thus infinite, but in a infinite amount of time one could count all of the numbers (this is not possible for human because we have finite time).

I don't think it's helpful to talk about what you could do in an "infinite amount of time", because like you said that's not possible, and it's not really obvious what we might be able to do given infinite time.

A more concrete way to talk about this is to say that, if we have a countable set of objects, we can come up with a way of listing them that will eventually reach any given object. For example, if we list the positive integers like 1,2,3,4,..., then you can pick any positive integer you like and it will show up in our list eventually.

> Continuous think of decimal pick two decimal call the larger one B and the sampler one A, then pick a decimal C; where C is in-between A and B, then repeat (C will now be B and one will pick another C) This will go one forever and you can always find another decimals that we didn't account for. One can't "count" all of the decimals because you can always pick another decimals between A and B.

But this just shows that your particular approach to counting them didn't work. Maybe there is a way of counting them that doesn't keep zeroing in on a smaller and smaller interval. In fact, for the set of all numbers with finite decimal expansions, there is a way.

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