Haha, constant introspection is indeed never a bad thing.

Not sure whether what I'm about to ask really qualifies under what's considered to be random in this thread, but is anyone having trouble with the Deviantart website? I can open the website, but none of the pictures load. It has also been happening since yesterday.

Just a question to those who open the website either sometimes or regularly. Thank you.

EDIT: IT'S FINALLY WORKING AGAIN! YESS!! You can ignore my question, thank you.

Random Question: How does GOG handle multiple editions of games in your library?

Reasoning; I have the Witcher 3 base game in GOG library (I believe I got it when GOG was gifting you games that you previously purchased on Steam), There is now a special on the Witcher 3 game and I would like to get the GOTY edition but I would prefer not to have two Witcher 3 games in my library.

Basically I am wondering should I just buy the DLC for the base which means only one Witcher 3 entry in my library or will the GOTY edition replace the base edition I currently have.

Hope this makes sense :D

If you buy both DLC you should automatically get the GOTY added to your account - additionally.

You can however "hide" games from your account, if that bothers you.

That sounds pretty normal to me. You're definitely not the only one. I am more focused and concentrated on a text if I read it silently as well. Like you already said, you have to concentrate on pronounciation in addition to everything else - so one more thing your mind is occupied with, and if you have an audience, perfectionism, self-consciousness or other feelings might distract you, too. And apart from that, if you read silently, you can read at your own speed and go back over something you didn't fully take in yet, whereas if you read aloud, you constantly push forward at a reasonable speed. It's more linear, you can't jump around that easily - frankly, it would probably be a pain to listen to how I read in my head. And there are people who attach imagery to words when reading, especially with fiction, who imagine the scenes described as if they were a movie. Not everyone is like that, maybe even just a minority, but I certainly am. And it also helps me to understand and remember text better, but it takes a little time and is harder to do when you have to concentrate on reading aloud at a constant pace, so everything read aloud is a little less clearly outlined and anchored in my head due to the lack of imagery.

In school or uni, when I was asked to read something aloud - especially in language classes -, I would often re-read it silently afterwards, to better understand what I had been reading there. It's not that I would not understand the text at all when reading it aloud, but I would pay somewhat less attention to the content and it made me feel like I might have missed something.

I can't agree more. And I think one of the main problems with having to read aloud is best explained by your explanation when you said that reading aloud requires you to read at a constant pace, which is true when your self-consciousness really takes over or when an audience is present (like you said).

Also, another funny thing that I assume people do when they want to understand what they're reading when they read aloud (again, just an assumption. Don't how much of it is true) is that funnily, they would try to stop for a quick while after each sentence, and silently reread what they have just read while overlapping the act with other things like taking a deep breath to act as a cover for what they're doing, and continue reading it again aloud. Take note, the situation that I was referring to is one where one or more audience is present to listen to whatever it is the person is reading (also in a school or uni setiing).

Is GOG changing the slug for Hitman: Codename 47 from 'hitman' to 'hitman_codename_47' reason to get excited?

If one divided by three is X, then why is X times three less than one? (0.9 recurring)

Because .9 repeating is 1.

One proof:
Let x = .999999... (repeating forever)
Then 10x = 9.999999...
Subtracting the first equation from the second, we get:
9x = 9.000000..., which is just 9.
Hence, x = 1.

Another proof, via infinite series:
.9 repeating is just an infinite series:
9 / 10 + 9 / 100 + 9 / 1000 + ... + 9 / 10^n * ...

This is a geometric series, with initial term 9/10 and common ration 1/10 < 1, so we can apply the formula:
(9 / 10) / (1 - (1/10)) = (9 / 10) / (9 / 10) = 1

Hence, in your example, X times 3 is indeed equal to one.

But...

Perhaps .9r is very close to one. But that's not equal. Keep adding 9's, and it will get closer and closer to one, but it will never actually reach equality because there will always be an error. You can always add another 9 on the end.

For example, if X = 1 - 0.9r, then you can divide a number by X and get a very large result. The more 9's you use, the larger the result. But you do get a result, therefore X cannot be zero and 1 cannot be equal to 0.9r.

I can see you know maths, and I'm sure you must be right. I just need to prove it to myself.

Try taking the limit. Let y be the number represented by a decimal point followed by n 9s. Now, take a look at the number you get if you let n approach infinity. If you do this, you'll find that y approaches 1, and that 1/y approaches positive infinity. Hence, the limit, which corresponds to the 9s repeating forever, is 1.

Wait, I need my coffee first!

A crude analogy:

I'm 6ft away from my door when I hear a knock. I move towards the door following this simple rule: Each step takes one second and covers half of the remaining distance. EG: After one second, I'm 3ft from the door. After two seconds, I'm 1.5ft from the door etc. How long will it take for me to reach the door?

Of course, I will never reach the door. Not after a trillion years. Never. No matter how many steps I take, there will always be half of the last step remaining.

It's the same if, instead of using 1/2 (0.5) per step, you use 9/10 (0.9) per step. You never reach the door, and 0.9r never reaches 1. Approaches, yes. Reaches, no.

0.9 is 0.1 less than 1.
0.99 is 0.01 less than 1.
And so on. Use n number of nines, the difference is always n-1 zeros followed by a 1.

An infinitesimal difference is still a difference.

In practical terms, 0.9r is as close to 1 as makes no difference. But in absolute logical terms, where 1 = true, and not 1 = false. Then 1/3*3=false.

In practice, one step takes not one second, but rather a number of seconds proportional to the distance moved. For example, maybe you move at one foot per second.

Then, the number of seconds it takes to take n steps will not increase without bound, and after 6 seconds you'll have taken the infinite amount of steps required to reach the door.

Let n be infinite. Then, after n (infinite) nines, the difference is an infinite number of zeros followed by a 1. Thing is, if we have a number like this, then every approximation of the number, no matter how precise, is 0, as you're never going to see the 1 at the end; therefore, that 1 doesn't come up. It's smaller than every positive number, so it has to be zero or negative (and negative can be ruled out).

By the way, if you *really* want that 1 to mean something, there are ways to describe that in mathematics:
* Transfinite ordinals. ω represents ordinal infinity, so ω + 1 represents the ordinality of an infinite sequence followed by 1 more element. (Note that this is different from transfinite cardinals, which are different.) In other words, this would like "follow this infinite path to the end, and once you reach it, turn left.
* For dealing with infinitessimals as actual mathematical objects, there's nonstandard analysis.

Give me a positive real number that is smaller than the absolute difference between .9 repeating and 1.

So we agree. 0.9r is approximately 1?