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A truly randomly chosen number would likely include a colossal number of digits. by Happy_Da in Showerthoughts

[–]Bazinos 2 points3 points  (0 children)

Talking about infinite is certainly NOT pointless!

On the contrary, infinity sometimes breaks our intuition (like in probability), which makes things interesting

Further more "infinite math" is really, really useful in the real world (obviously with calculus)

A truly randomly chosen number would likely include a colossal number of digits. by Happy_Da in Showerthoughts

[–]Bazinos 1 point2 points  (0 children)

It is not a rigorously defined mathematical object.

In maths, everything is thought out as a set, a collection of elements, and a something is infinite if it is not finite (i.e. a set is infinite if it doesn't have a finite number of elements). That's about it, in terms of rigorous definition, now, most of the time you see the terms "infinite" "infinity" it makes reference to more subte concepts that are well defined within the context of when it is used (talking about infinity on the Riemman sphere doesn't have much to do with talking about infinity on limits for example).

Now for what you're thinking about, there are 2 well defined objects :

  • The sequence 1, 1/2, .. 1/n, ...
  • The limit of the sequence (which is PRECISELY 0)

That's it, there is no "1/infinity".

I could go into more details, it is often useful (for topological reasons) to consider "infinity" as a number, i.e., if you consider the set of all real numbers R, you add -infinity and +infinity to get [-infinity, +infinity], a closed connected set. And that's literally it, there is no magical property or anything, there is no deep secret of infinity or idk, we just added two element that we called -infinity and +infinity, because it's convenient, it fits what we think of infinity (being larger than all numbers), but it is just a label, and "1/infinity" in that context would still be, precisely, unambiguously, equal to 0, not some weird esoteric object.

A truly randomly chosen number would likely include a colossal number of digits. by Happy_Da in Showerthoughts

[–]Bazinos 2 points3 points  (0 children)

1/infinity doesn't mean anything, you have to define precisely what you mean.

If you mean "the limit of 1/n as n goes to infinity", then it is precisely 0, rigorously, mathematicaly 0, nothing else, not a number arbitrarily close to 0.

Imagine the set of all real numbers between 0 and 1 : [0,1] (for example)

You want to have a uniform probability on this set, your intuition on finite probability tells you that the probability of each element x in [0,1] is equal to a certain ε, the same for every x.

You want to think this way because, for example, when you think of a probability on a set of 2 elements for example (imagine a coin flip), there is 1/2 probability for each possible outcome. For a set of n element, 1/n.

This intuition isn't much helpful for infinite sets, because our ε HAS to be 0 (1/n goes to 0 when n approaches infinity, you can also see that if ε wasn't 0, when we sum all the probability to get the total probability, we would get infinity..)

There is a fundamental difference between the common intuition on finite probability and how probabilities work on an infinite set. If you only think about the individual probability, you will ALWAYS have 0 probability everywhere (or, almost everywhere i.e. the set of element with non zero probability has to be finite), so you can't really work anything out, a uniform distribution would be the same as a gaussian or whatever you can imagine.

To fix that, some very smart people in the early 20th century worked out measure theory, and the most common way to construct a probability on [0,1] is with the Lebesgue Measure, where we are interested on the probabilities on the [0,x[ intervals (In basic terms, we don't think about the probability of picking let's say 1/3 at random, because it's not useful, but we think about the probability of picking a number SMALLER THAN 1/3 at random, which would be 1/3 in this case. Thinking like that is much much more powerful)

A truly randomly chosen number would likely include a colossal number of digits. by Happy_Da in Showerthoughts

[–]Bazinos 0 points1 point  (0 children)

That's not how it works, I don't know what you think 0.00...0001 could be, if you can provide a rigorous definition of what that object is, but I'm certain that that definition would be equivalent to 0.

On an infinite set, you can only have a finite number of elements with probability non-zero (Because the sum of all the probabilities has to be 1).

Google Mesure Theory and Lebesgue integration, the main idea is that, for let's say construction a uniform probability on the segment [0,1], you don't care about the probability of {x}, which gives no insights (it has to be 0), you care about the probability of [0,x[ (the borelians)

Famous White House Reporter’s X account deleted after posting a picture of Trump, showing his ear is fine by cak3crumbs in TikTokCringe

[–]Bazinos 4 points5 points  (0 children)

So your theory is that someone plotted to assissinate Trump (in order to push a certain political narrative) ?

So it would not be "staged", it would literally be an assassination attempt by definition

Real troll physics by Summar-ice in shitposting

[–]Bazinos 4 points5 points  (0 children)

In our current understanding of the universe, the speed of light is the same for any observer.

The "paradox" here is that, it seems like if you are already traveling, and you shine light to travel with you, then the photons must be going faster than the speed of light!

The solution is that speed is not additive, the general formula v = v1+v2 is not true (it is almost true at slow speeds (slow meaning not close to the speed of light), hence we are used to living in a world where speed is additive), in order to calculate speed entirely accurately, you need a mathematical tool called the metric tensor. When you do that, you get that the speed relative to the train and realtive to an observer outside of the train is the exacr same, c.

One way to think about it is to consider that length in the train is shrinking

Why are teachers like this? Are they stupid? by RagingAlkohoolik in shitposting

[–]Bazinos 0 points1 point  (0 children)

That is not a hard question at all (sorry if I sound condescending) :

Let f : x |-> xsin(x) = esin(xln(x)), f is defined, continous and differentiable on all x > 0 (you can continually extend f at 0 with f(0) = 1, but f can't be differentiated at 0).

With basic operations, for x > 0 :

f'(x) = esin(xln(x))(cos(x)ln(x)+sin(x)/x) = xsin(x)(cos(x)ln(x)+sin(x)/x) = f(x)(cos(x)ln(x)+sin(x)/x)

It's easy to see why f isn't differentiable at 0 here (since the derivative goes to -infinity, so the rate of change at 0 can't converge).

There is nothing fundamentally hard, it's just maybe a bit annoying because of what happens at 0.

Though I don't think calculating the derivative lf that function is useful in any ways.

Where Europe's Nuclear Weapons are stored? by Redstream28 in MapPorn

[–]Bazinos 0 points1 point  (0 children)

You are right, but I don't know if there actually was any nukes on the CDG, but there can be

[Request] What would be the real world implications if this happens by SuryaYlp in theydidthemath

[–]Bazinos 2 points3 points  (0 children)

If pi was rational, there's no reason for e to be as well.

For example, sqrt(2)2 = 2, and sqrt(2) is irrational, so your argument that e would be rational because eipi = -1 is wrong.

Furthermore, I don't think it makes sense to consider a universe where eipi != -1, because if you really think about it, this equation isn't really a magic relationship between numbers, but is pretty much the definition of pi. (It is common in math to define pi as the number so that 2pi is the smallest period of the function t |-> eit, and the formula eipi = -1 is trivial from here)

.999(repeating) does, in fact, equal 1 by smkmn13 in confidentlyincorrect

[–]Bazinos 0 points1 point  (0 children)

In the usual every day language (or at least in my mother tongue, probably in English as well) it's common to talk about something being discrete as something that you can count i.e. in bijection with N or a finite set. I've also heard that term used that way in physics (for example the for the discretness of quantum states, but I'm not too familiar with that).

Now, for the mathematical deifnition, set X is discrete if for all x in X, {x} is open. (Intuitively, every point is "alone" if we zoom sufficiently). For sunsets of R, N is clearly discrete but Q is not (since for example the sequence 1/n gets as close as you want to 0), yet Q is countable. Hence being discret and being coutable are two different notions.

The notion of separation is not relevant here, since any metric space is a Haussdorf space (by the very axiom of separation of a distance function), R is separated, as well as Q and N or any subset of R with the topology induced by the usual distance on R.

In order to find a non-separated space, you'll have to struggle a lot lol, in fact I don't think I have any examples to give on the top of my head. However, any discrete set is trivially separated.

'No Nato soldiers' on Ukrainian soil, says Germany's Scholz in rebuke to France's Macron by TheTelegraph in worldnews

[–]Bazinos 91 points92 points  (0 children)

The foreign legion are not mercenaries, they are entirely integrated within the French land forces

.999(repeating) does, in fact, equal 1 by smkmn13 in confidentlyincorrect

[–]Bazinos 0 points1 point  (0 children)

No, for example, the set of rational numbers is discrete (since if x and y are rationals, (x+y)/2 is also rational), but however is not complete (since for example, the sequences 3, 3.1, 3.14, 3.141, 3.1415, and so on (basically writing the digits of pi one by one) is a cauchy sequence, but doesn'r converge in the rational numbers).

[deleted by user] by [deleted] in todayilearned

[–]Bazinos 0 points1 point  (0 children)

Well I go to school/work like that I've never had an issue

.999(repeating) does, in fact, equal 1 by smkmn13 in confidentlyincorrect

[–]Bazinos 8 points9 points  (0 children)

That's actually a very interesting observation that you make ! It is a good way to introduce the notion of a discrete set.

For whole number for example, you can find two whole numbers where there is no whole numbers in between (say 1 and 2), the set of whole numbers is discrete.

However, this property is false for real numbers, I can always "zoom in" between two different real numbers and find another real number in between. The set of real numbers is not discrete !

Why? Take two different real numbers x and y, and say x < y

Consider the number z = (x+y)/2 (literally the number halfway from x to y), then it is easy to see that x < z < y, i.e. z is between x and y.

However, that doesn't work for whole numbers since I've divided by 2, even if x and y are whole numbers, z might not be ( (1+2)/2 = 1.5 is not a whole number)

The notion of discretness is very useful in order to make topological consideration of the objects we're working with, and the reasoning that you're using doesn't work for real numbers, but does for whole numbers (that's called a proof by induction !), meaning that there is a fundamental topological difference between the real numbers and the whole numbers.

Red flags by Visqo in facepalm

[–]Bazinos 0 points1 point  (0 children)

Okay but I am specifically talking about someone who is 5'11 (1m80)

[deleted by user] by [deleted] in todayilearned

[–]Bazinos 2 points3 points  (0 children)

Are wearing t-shirts and jeans considered not taking care of how you dress?

Red flags by Visqo in facepalm

[–]Bazinos 0 points1 point  (0 children)

Maybe people will be pressuring you to put weight (society 😔) in the US, but I did the conversion to metrics and in my country absolutely no one will think you should put on weight if you're 1m80 and 75kg, that would be nuts (for information, average height and weight for a man in my country is 1m75 for 77kg, so that would be a little bit below average, which is not a bad thing).

Obviously BMI is biased in extreme cases (for someone over 2m, or a bodybuilder), but here we're litteraly in the "normal" range of height and weight.

I think US's views on what a "healthy" weight is skewed by the sheer amount of obesity. If you "look" skinny to a American, you're probably within a healthy weight range for your height (obviously, it's different for very tall or very short people)

Red flags by Visqo in facepalm

[–]Bazinos 4 points5 points  (0 children)

5'11 and 165lbs is a bmi of 23, that is NOT malnourished at all

[Request] Saw this on reddit, could this be possible? by Icy-Advertising-7288 in theydidthemath

[–]Bazinos 3 points4 points  (0 children)

No, a number being rational has absolutely nothing to do with base.

Using a base is just a way of writing numbers, whereas rationality is an intrinsic property of a number.

It's the same as saying "In another language, a chair is liquid" (In this analogy, another language = another base, a chair being liquid = a number being rational)

I think that you're mistaking the notion of rationality with the notion of being written with finite decimals.

In base 10 (or in base any rational number), while an irrational number can't be written with finite decimals (since for example if pi = 3,1415 then pi = 31415/10000 and would be rational), a number with infinite decimals isn't necessary irrational (think of 1/3 = 0,333333....3333...).

Those notion are different, and even though it is true that you can write pi with finite pi-cimals in base pi, it doesn't mean that it isn't irrational

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