I have the below chunk of code. My goal was to show students how any number, divided by half, will never reach zero. (Zeno's Paradox. If you step halfway towards a wall with each step, you can never reach the wall.)

However, the below chunk of code reaches 1 and divides down to 0. Instead of reaching 1 and dividing to .5, then .25, then .125, et al...

 import random
 def half(number): 
    for i in range(1, 30): 
            print(number // 2)
            return(number // 2) 

n = random.randint(1, 1000000)
while n !=0:
    n = half(float(n))

 

Sample Output
293763.0
146881.0
73440.0
36720.0
18360.0
9180.0
4590.0
2295.0
1147.0
573.0
286.0
143.0
71.0
35.0
17.0
8.0
4.0
2.0
1.0
0.0

Corrected code

import random

def half(number): 
            print(float(number) / 2)
            return(float(number) / 2)

n = random.randint(1, 1000000)

for i in range(1, 30):
            n = half(float(n))

With expected output of 30 lines, passing 0, and continuing on to 0.000001487

I am reading A Treatise on Human Nature and got stuck on his argument why time must be composed of indivisible moments. In particular, I don't understand how he relates the existence of indivisible moments as an idea to the, what seems to be, objective existence of indivisible moments of time. Why is this an adequate representation of reality and not just a limitation of our mind? I suppose that because our mind is a computer, it requires a minimum time to do a computation which means we could never experience infinite divisibility and therefore never create an idea of infinite divisibility.

I'm reading Hume by myself and would also appreciate any references that could help me through his work when I get stuck in the future, if anyone could provide those.

For positive integers a and b, a^n + n | b^n + n holds for all positive integers n. Show that a = b.

EDIT: +n instead of +1

Is it possible? On a similar note, can something be infinitely small, like a singularity? Infinitely large? Is infinity actually something that's possible? I was having a philosophical conversation with someone and they mentioned that something could not be infinitely divided because it would cease to exist. This didn't really make sense to me because of my previous knowledge of singularities, universe expansion, etc., but I couldn't support my side with evidence. Help?

Edit: Answered thanks!

I don’t know if I’m explaining this very well.

If the idea behind the electoral college is that the president should have a majority of the small states AND a majority of the big states, so they care about the interests of both small states and big states, as opposed to a candidate getting all his votes from big states and no supporters in small states and he enacts all the big states ideas and none of the small states ideas.

WHY is the only division that matters between big and small states? Why is that division more important than any other?

I mean we could divide Americans into male and female, divide them by race, religion, urban vs rural, or any other categorization. Then we could say, the president should get a majority of white people, a majority of black people, a majority of men, a majority of women, a majority of Christians, a majority of Muslims, a majority of atheists…

(Well not strictly a majority in EVERY category, but they should get a substantial fraction of the vote in every category.)

Because they should represent every individual category’s wants. Does this make sense? Obviously this would be way too complicated to actually do, but what I’m asking with this hypothetical scenario is, what makes the division between large and small states any different from any other category?

Edit: let me explain what I mean with an example. America is like 70% Christian, so if a candidate appealed to solely Christians, they could win 70% of the vote and win. Then we could say, that’s bad because the president is enforcing Christian ideas against the 30% who aren’t Christians! He should care about the interests of both Christians and every other religion.

Theoretically, if I released a coin that had no limit to the number of decimal points I could fractionalise it into, wouldn't it be a coin of infinite supply?

I'd call it, THE ABSOLUTE UNIT. There would be only one in supply. Ever. And I'd do an ICO in which I sell investors NanoClits ( a billionth of the ABSOLUTE UNIT).

I'm curious what price action would look like. Would the ABSOLUTE UNIT be worth infinite dollars per coin, or zero? It's kinda like a divide by zero situation. The Math just breaks.

i just wanna screw around conquer the world as tuva or something im to stupid to win even on civilion so i just need a mod

Is there anything in BTC's protocol forcing a minimum size? Or can BTC be divided into .00000000000000001 units of BTC and so on?

Quick update for anyone wondering about an answer: BTC can be divided to 8 decimal places based on transaction capabilities. Protocol can be modified if needed. Thanks to u/ajpwahqgbi.

Edited out cuz I got the answer I needed and this is making people's heads spin. Just no time to discuss the theoretical stuff.

Someone on Twitter asked how to explain Bitcoin to someone who says it’s just the “greater fool’s” theory. This is how I thought about it. Thoughts?

Wowhead link

This is my only reasonable choice from weekly chest, so I'm considering whether it's worth using

This trinket used to be really bad, not scaling with any stats, but it seems to be fixed now, scaling at least with crit and vers. It sims reasonably well, being 3rd equip (not on use) trinket in sims on both patchwerk and hectic cleave, behind Stone Legion Heraldry and Hateful Chain. The latter sims significantly better than real performance in most cases.

Is 226 Ooze worth taking with one of the top on use trinkets, or would it be better to play with lower ilvl double on use instead (like PvP Badge for example)?

Balancing games is often like trying to shoot a moving target, I get it.

But Massive has had the same formula for The Division series ever since the days of TD1 plus an entire year of TD2 feedback. The core gameplay reward loop hasn't changed (grind, kill, collect loot, repeat). All they had to do was refine certain aspects of the game to make grinding loot more rewarding. But for some odd reason, many gameplay mechanics have completely reverted back to the same exact state that garnered a shitstorm of negative feedback closely following the initial release of TD2 one year ago --- namely, over-aggressive AI, overtuned enemy HP/damage, skill builds not being worthwhile to build, etc.

I don't for a second believe that I'm entitled to any overnight balance changes, or even a perfectly balanced game to start with. I enjoyed the $30 I spent for WoNY's storyline content. But the reality is, I find developer comments like these pretty tone-deaf: Posted by ChrisGansler on 3/10/2020 9:50:00 AM:

>I think that's not really fair. We have talked about the game difficulty as early as last week on State of the Game. What we don't want to do is go back to the difficulty levels of TD2 before the expansion. If we blanket nerf everything we likely will have to follow-up with blanket buffs afterwards. We don't believe it's the right way to go.

>If you feel that a week is not quick enough, when a majority of the player base hasn't even reached the max level, then I can't offer you exact changes for everything yet. If you believe you need to take a break because you're not enjoying yourself that's totally fine. I just want to say again that stopping to play to proof a point doesn't really do anything to speed up our processes. Software development, especially balance, takes time.

Game developers often have only 1 chance to make a first-impression. And Massive has had many chances at first impressions already. All I can say is, Division 2 isn't the only game on the block. Once some players leave, you've forever lost their future business.

https://preview.redd.it/vli0ofqwf6w71.jpg?width=3840&format=pjpg&auto=webp&s=2a704c47375637858c27216379ae8313dadf8be8

This could be a long read. Kindly bear with me.

I write this primarily in response to the TechSpot article from yesterday (r/technology mods told me they only allow “mainstream news articles with editorial oversight and fact-checking” so I'm sharing this here).

But I’d also like to take this opportunity to write about Bitcoin more broadly as someone who has been following it for more than a decade and I’ll try to do so without complicating the conversation for anyone unfamiliar with Bitcoin.

The TechSpot article cites a non-peer-reviewed National Bureau of Economic Research (NBER) working paper from Igor Makarov and Antoinette Schoar.

NBER claims to be non-partisan but it is a private NPO funded by the likes of Bill Gates foundation.

The chairman of NBER, Karen Horn, is a former president of the Federal Reserve Bank of Cleveland and Head of International Private Banking for Bankers Trust.

The authors of this working paper, Igor Makarov and Antoinette Schoar are no experts in Bitcoin.

Makarov is employed by Financial Markets Group (FMG), which focuses on policy research into financial markets and works alongside banks and regulators in Europe.

Schoar is a professor at the MIT Sloan School of Management and co-chair of NBER Corporate Finance group, who has previously made it clear that she is no fan of Bitcoin with some pretty misguided takes on it.

It’s critical to note that the data regarding miners cited in this study is from when mining was largely concentrated in China. This is no longer the case.

The paper claims the authors have “the ability to trace miners on the blockchain.” The tracking method shown in the paper is based on subjective, unverified “algorithm to track the distribution of mining rewards from the largest 20 mining pools to the miners that work for them.”

The validity of this conjectural method of tracking was also subjectively verified before all mining operations migrated out of China to many different parts of the world.

Natural numbers with multiplication are a partially ordered monoid via the divisibility relation in a natural way, with 1 being the least and 0, which is divisible by anything, the greatest element. This partial order is also a complete lattice, with gcd and lcm as finite infima and suprema, and 0 the supremum of any infinite subset. In particular, with this ordering we have lim_n a_n = 0 for any strictly increasing sequence, and ΠA = 0 for any infinite set A.

The lattice of ideals of Z is the mirror image of this, so any way of saying "(0) is the smallest ideal" is basically saying "0 is the largest integer (in this particular sense)", but I was idly wondering if there are more interesting or surprising contexts where you get behavior that looks kind of like e.g. lim_n p^n = 0 or Π_p p = 0? Statements like "if P is true mod n for infinitely many n, then P is true mod 0" should also qualify, but I don't know if there are interesting examples with this generality, instead of the weaker versions with "... true mod p for every prime p" as the condition.

Imaginings of the past and future are harder to bear than the present moment.

"Do not disturb yourself by imagining your whole life at once. Dont' always be thinking about what sufferings, and how many, might possibly befall you. Ask instead, in each present circumstance: "What is there about this that is unendurable and unbearable?", You will be embarrassed to answer"

Marcus Aurelius, Meditations 8.36

"Think about individuals; consider men in general; there is not one whose life is not focused on tomorrow. What harm is there in that you ask? Infinite harm. They are not really living. They are about to live"

Seneca, Epistles 45.12-13

[first] [prev] [next]

Never forget that before your op is someone else's op, that while you're doing your run someone else is making their run, and after your run there is another beginning or doing their run. - Street Solo advice, Fighting Man's Magazine, Resource War Era, TerraSol.

Speaks blew the android's head off with his SMG, grabbing the body and yanking it out even as he leveled the SMG at the creation engine's computer system and pulled the trigger. The SMG had a whistling noise and Speaks knew the barrel was almost shot out.

The light SMG, firing 2.2mm rounds, was supposed to only see a few bursts worth the work, maybe one or two mags.

Speaks had burned through almost a dozen mags and the memory-plas was badly worn.

The android crashed to the ground and Speaks patted him down. He was carrying a heavy battle rifle, high caliber, loaded with heavy mass reactive gyrojet rounds, with an underslung 20mm variable munition grenade launcher. Speaks stripped grenades off the android's harness, checking them over and tucking them into his own gear.

A quick glance outside the conex showed that nobody was close and he scurried across and down a narrow gap between conex stacks. Lights stabbed down, searching through the conex containers and the equipment of the shipping yard. Speaks looked up and saw hovercraft in the air, some marked with LawSec and others marked with news stations.

"No, you idiots," Speaks swore, running for the fence.

That instinct raised up again and Speaks threw himself to the side, rolling, and a loud KARAK! sounded out right before a crater was blown out of the ferrocrete right where he would have been.

Speaks dropped a grenade as he rolled, coming up on his three feet and running for the conexes. The sniper was on the upper level highway access.

The sniper round blew through his shield and came so close that the air displacement ripped the end of his left antenna off. Speaks staggered, slapping his camo and putting on a burst of speed.

In the sky two of the LawSec HRT and one of the news hovercraft exploded. The unarmored news hovercraft fell to the ground, a burning hulk erupting in flames, the two HRT craft falling from the sky and slamming into the ground, the high-G impact killing the crews.

Speaks put on a burst

Given

#include <iostream>
#include <map>
using namespace std;

int main()
{
    double a;
    char op;
    double b;
    map<int, string> errorCodes;
    errorCodes[1] = "DivisionByZero Error\n";
    errorCodes[2] = "FloatAsModuloArgument Error\n";
    int result;
    bool flag = true;

    while (flag) {
        double error = 0;
        cin >> a >> op >> b;
        switch (op)
        {
            case '+':
                cout << a + b << '\n';
                break;
            case '-':
                cout << a - b << '\n';
                break;
            case '*':
                cout << a * b << '\n';
                break;
            case '/':
                //exp ? exp : exp
                b != 0 ? result = (a / b) : error = 1;
                error == 1 ? cout << errorCodes[error] : cout << result << '\n';
                break;
            case '%':
                a - (int)a == 0 && b - (int)b == 0 ? result = (int)a % (int)b : error = 2;
                error == 2 ? cout << errorCodes[error] : cout << result << '\n';
                break;
            case 'e':
                cout << "Exiting mini-calc";
                flag = false;

        default:
            cout << "that's not a valid operator guy, try Texas Instruments(TM)\n";
            break;
        }
    }
}

The following inputs are valid:

1+10
11
3*8
24
4-10
-6
10/2
5
10%3
1
10/7
1
7.4%6.44
FloatAsModuloArgument Error
34/0
DivisionByZero Error

This input causes an infinite loop:

a//b

Where a and b are arbitrary floats or ints.

34//5
DivisionByZero Error
DivisionByZero Error
DivisionByZero Error
DivisionByZero Error
DivisionByZero Error
DivisionByZero Error
...

Why?

I think I understand how inflation can come from fiat central banks printing money to increase the supply. But if we can divide Bitcoin into arbitrarily (effectively infinitely?) small amounts, isn't that the same as an infinite supply? I am missing something when they say Bitcoin is deflationary.

How can a good store of value (SoV) also be a good medium of exchange (MoE) and unit of account (UoA)? Seems too perfect, right?

If the goal of Bitcoin is to replace fiat money, but Bitcoin is expected to increase in value in the long term, wouldn't it be prohibitive to use Bitcoin for paying for things?

This perspective comes from measuring Bitcoin's value in an inferior, depreciating form of money, and stems largely from a collective price illusion that the dollar is a stable representation of monetary value. The dollar price of Bitcoin is merely relative face value, rather than intrinsic value, while Bitcoin, as a nascent form of money, still very much remains in the process of discovering its true value to humanity.

You could indeed argue that it's humans who are in the process of learning to appreciate its value. Bitcoin is quite the monetary paradigm shift.

What is money?

Money is anything that's accepted as representing value by the parties to any transaction. It's really that simple. Three thousand years ago, cowrie shells were used to represent value. Humans have always sought money that can hold value over time until it was required to purchase other things that hold value to them - goods and services.

When you purchase goods and services now, the question you ask yourself is whether what you're purchasing is valuable enough to you that you're happy to part with a certain amount of dollars to acquire it. Everything being denominated in dollars/fiat money lends to this perspective that the dollar represents some value that can be exchanged to buy things you need in life.

When we get to a place where satoshis (sats) replace dollars as UoA, it would be a question of whether the good/service you're purchasing is necessary/valuable enough to you that you're happy to part with a certain amount of sats to acquire it.

But the supply is finite and limited to 21 million. Is this not a problem? It's finite but divisible. Injecting new money into the economy, as central banks do, is just an artificial way of re-dividing the aggregate monetary value within the economy inequitably, in favor of those close to the new money.

Sure, there aren't enough bitcoins to go around for everyone, but there are more than enough sats (units of money) to go around for everyone, ~ 2.1 quadrillion sats.

For context, the total value of all the physical money and money deposited in savings and checking acco

Regarding this WSJ unfounded FUD:

https://www.wsj.com/amp/articles/bitcoins-one-percent-controls-lions-share-of-the-cryptocurrencys-wealth-11639996204

Credit for post and DD goes to u/xcryptogurux

Original post here:

No, Bitcoin is not controlled by a small group of investors and miners (A rebuttal to the TechSpot article)

It is well documented that Bitcoin is not centralized, in any way.

Here's a Glassnode thorough analysis regarding distribution:

https://insights.glassnode.com/bitcoin-supply-distribution/

Highlights:

> No, Bitcoin Ownership is not Highly Concentrated

> 1. Not all Bitcoin addresses should be treated equal. For instance, an exchange address holding the funds from millions of users needs to be distinguished from an individual's self-custody address. > > 2. A Bitcoin address is not an "account". One user can control multiple addresses, and one address can hold the funds from multiple users.

Edit: Also this info from Woo

This is good for Bitcoin.

> Willy Woo on Twitter:

> A longitudinal study of #Bitcoin's supply distribution since the genesis block. > > Summary: > > Bitcoin continues a 12 year trend of distributing evenly. Small holders are a rising force. (Includes new data unseen before from Entities, not addresses on-chain analysis.)

https://twitter.com/woonomic/status/1418192184767963136

> https://preview.redd.it/vli0ofqwf6w71.jpg?width=3840&format=pjpg&auto=webp&s=2a704c47375637858c27216379ae8313dadf8be8 > > This could be a long read. Kindly bear with me. > > I write this primarily in response to the TechSpot article from yesterday (r/technology mods told me they only allow “mainstream news articles with editorial oversight and fact-checking” so I'm sharing this here). > > But I’d also like to take this opportunity to write about Bitcoin more broadly as someone who has been following it for more than a decade and I’ll try to do so without complicating the conversation for anyone unfamiliar with Bitcoin. > > The TechSpot article cites a non-peer-reviewed National Bureau of Economic Research (NBER) [working paper](https://www.nber.org/pape