Bitcoin Forum
May 03, 2024, 04:32:34 PM *
News: Latest Bitcoin Core release: 27.0 [Torrent]
 
   Home   Help Search Login Register More  
Pages: [1]
  Print  
Author Topic: Hashrate and Difficulty Adjustment  (Read 177 times)
Yogee (OP)
Sr. Member
****
Offline Offline

Activity: 1540
Merit: 412



View Profile
November 23, 2020, 04:49:25 AM
Last edit: November 23, 2020, 05:47:56 AM by Yogee
Merited by Halab (2), Yaunfitda (1), DdmrDdmr (1)
 #1


- https://bitcoin.clarkmoody.com/dashboard/

Bitcoin tech geeks knows how to read what the image above means or interpret the data but most newbies probably don't so I'm just gonna lay some basic information for them and ask questions myself about certain subjects that's not clear to me yet. Feel free to correct my inaccuracies or add more to the topic as always.

Basics
- Each block was designed to be mined every 10 minutes [Block Time].
- New computers machines that can perform calculations faster [Hash Rate] can mine new bitcoin faster.
- Mining difficulty is adjusted every 2,016 blocks to bring back the block time to normal [10 minutes].
- The 2016 blocks are expected to be mined in two weeks [calculated using 1 block per 10 minutes].

Using the example above, the current time it takes to mine a block on average is about 9 mins and 18 secs which is shorter than 10 mins. The next difficulty adjustment is scheduled on Nov. 29, 2020 and there are 973 blocks left before it reaches 2016. Since mining seems faster, the mining difficulty is expected to increase by 12.9% to bring block time back to 10 mins.

Please note that there are times when the total hashrate drops since some miners may decide to turn off their machines at any point in time. As a result, mining for each block could be longer than 10 mins and the difficulty will be reduced for the same reason when another 2016 blocks are mined after the last adjustment. The drop could encourage miners to turn on their machine and join the mining business again and we can expect hash rate to increase should that happen.

Other points
- There are some people who associate drop in hash rate to drop in btc price and vice versa but that's still speculation.
- The increase [decrease] in hash rates and mining difficulty is directly related to the network fees you pay. The faster the mining, the faster the mempool is cleared. Meaning transactions are mined faster [higher fees first] which allows txs with lower fees to be added on the next block sooner.

Question
- I don't understand what the "Difficulty Epoch" and "Block Time, Diff. Epoch" are for. Please explain as if I'm a total beginner hehe.

R


▀▀▀▀▀▀▀██████▄▄
████████████████
▀▀▀▀█████▀▀▀█████
████████▌███▐████
▄▄▄▄█████▄▄▄█████
████████████████
▄▄▄▄▄▄▄██████▀▀
LLBIT|
4,000+ GAMES
███████████████████
██████████▀▄▀▀▀████
████████▀▄▀██░░░███
██████▀▄███▄▀█▄▄▄██
███▀▀▀▀▀▀█▀▀▀▀▀▀███
██░░░░░░░░█░░░░░░██
██▄░░░░░░░█░░░░░▄██
███▄░░░░▄█▄▄▄▄▄████
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
█████████
▀████████
░░▀██████
░░░░▀████
░░░░░░███
▄░░░░░███
▀█▄▄▄████
░░▀▀█████
▀▀▀▀▀▀▀▀▀
█████████
░░░▀▀████
██▄▄▀░███
█░░█▄░░██
░████▀▀██
█░░█▀░░██
██▀▀▄░███
░░░▄▄████
▀▀▀▀▀▀▀▀▀
|
██░░░░░░░░░░░░░░░░░░░░░░██
▀█▄░▄▄░░░░░░░░░░░░▄▄░▄█▀
▄▄███░░░░░░░░░░░░░░███▄▄
▀░▀▄▀▄░░░░░▄▄░░░░░▄▀▄▀░▀
▄▄▄▄▄▀▀▄▄▀▀▄▄▄▄▄
█░▄▄▄██████▄▄▄░█
█░▀▀████████▀▀░█
█░█▀▄▄▄▄▄▄▄▄██░█
█░█▀████████░█
█░█░██████░█
▀▄▀▄███▀▄▀
▄▀▄
▀▄▄▄▄▀▄▀▄
██▀░░░░░░░░▀██
||.
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
░▀▄░▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄░▄▀
███▀▄▀█████████████████▀▄▀
█████▀▄░▄▄▄▄▄███░▄▄▄▄▄▄▀
███████▀▄▀██████░█▄▄▄▄▄▄▄▄
█████████▀▄▄░███▄▄▄▄▄▄░▄▀
███████████░███████▀▄▀
███████████░██▀▄▄▄▄▀
███████████░▀▄▀
████████████▄▀
███████████
▄▄███████▄▄
▄████▀▀▀▀▀▀▀████▄
▄███▀▄▄███████▄▄▀███▄
▄██▀▄█▀▀▀█████▀▀▀█▄▀██▄
▄██▄██████▀████░███▄██▄
███░████████▀██░████░███
███░████░█▄████▀░████░███
███░████░███▄████████░███
▀██▄▀███░█████▄█████▀▄██▀
▀██▄▀█▄▄▄██████▄██▀▄██▀
▀███▄▀▀███████▀▀▄███▀
▀████▄▄▄▄▄▄▄████▀
▀▀███████▀▀
OFFICIAL PARTNERSHIP
FAZE CLAN
SSC NAPOLI
|
1714753954
Hero Member
*
Offline Offline

Posts: 1714753954

View Profile Personal Message (Offline)

Ignore
1714753954
Reply with quote  #2

1714753954
Report to moderator
1714753954
Hero Member
*
Offline Offline

Posts: 1714753954

View Profile Personal Message (Offline)

Ignore
1714753954
Reply with quote  #2

1714753954
Report to moderator
Every time a block is mined, a certain amount of BTC (called the subsidy) is created out of thin air and given to the miner. The subsidy halves every four years and will reach 0 in about 130 years.
Advertised sites are not endorsed by the Bitcoin Forum. They may be unsafe, untrustworthy, or illegal in your jurisdiction.
1714753954
Hero Member
*
Offline Offline

Posts: 1714753954

View Profile Personal Message (Offline)

Ignore
1714753954
Reply with quote  #2

1714753954
Report to moderator
ranochigo
Legendary
*
Offline Offline

Activity: 2954
Merit: 4165


View Profile
November 23, 2020, 05:04:18 AM
Merited by dbshck (4), DdmrDdmr (1), Yogee (1)
 #2

There is no accurate way to ascertain the hashrate of the network as there's no data available. When you're looking at the hashrate displayed by the websites, it's usually derived from the block intervals of the blocks and the accuracy of that doesn't usually matter, so keep that in mind.

Epoch simply means the period of time so difficulty epoch is the n-th difficulty period, with n being an integer which signifies the number of difficulty adjustment that has occurred. The other block time, difficult epoch is the avg block interval in the current difficulty period.

The difficulty is adjusted based on the "block interval of the current difficulty epoch" (or the past 2016 block at the point of difficulty adjustment), so it'll be more accurate to refer to that metric as compared to the avg interval of the previous 2016 block.

Having a relatively long block interval over a period of time doesn't mean that the miners have turned off their ASICs, it could just be varience affecting it.

.
.HUGE.
▄██████████▄▄
▄█████████████████▄
▄█████████████████████▄
▄███████████████████████▄
▄█████████████████████████▄
███████▌██▌▐██▐██▐████▄███
████▐██▐████▌██▌██▌██▌██
█████▀███▀███▀▐██▐██▐█████

▀█████████████████████████▀

▀███████████████████████▀

▀█████████████████████▀

▀█████████████████▀

▀██████████▀▀
█▀▀▀▀











█▄▄▄▄
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
.
CASINSPORTSBOOK
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▀▀▀▀█











▄▄▄▄█
Steamtyme
Legendary
*
Offline Offline

Activity: 1540
Merit: 2036


Betnomi.com Sportsbook, Casino and Poker


View Profile WWW
November 23, 2020, 05:08:15 AM
Merited by DdmrDdmr (1), Yogee (1)
 #3

Here is a thread I wrote a while ago that covers more the mining side of things and helps people figure out if mining is for them. Most of these statistics don't mean anything to the general BTC public, apart from th eodd long block contributing to network congestion.
First time/Small miner reference for getting started.

To answer some of your questions

Basics
- Each block was designed to be mined every 10 minutes [Block Time].   On average
- New computers that can perform calculations faster [Hash Rate] can mine new bitcoin faster. Not new computers. We are way beyond that they are Asic chip machines mining BTC
- Mining difficulty is adjusted every 2,016 blocks to bring back the block time to normal [10 minutes]. The increase or decrease is proportional to how far off the average time of 10 minutes/block is
- The 2016 blocks are expected to be mined in two weeks [calculated using 1 block per 10 minutes].


Quote
Please note that there are times when the total hashrate drops since some miners may decide to turn off their machines at any point in time. As a result, mining for each block could be longer than 10 mins and the difficulty will be reduced for the same reason when another 2016 blocks are mined after the last adjustment. The drop could encourage miners to turn on their machine and join the mining business again and we can expect hash rate to increase should that happen.
There is rarely an event like this. Hashrate is so large at the moment it would take a catastrophic event to impact it with any large significance. Every year there is a bit of a swing around rainy season chinese miners turning on and off gear as the season comes to pass, even this doesn't really affect thing.
Quote
I don't understand what the "Difficulty Epoch" and "Block Time, Diff. Epoch" are for.

Other points
- There are some people who associate drop in hash rate to drop in btc price and vice versa but that's still speculation.
- The increase [decrease] in hash rates and mining difficulty is directly related to the network fees you pay. The faster the mining, the faster the mempool is cleared. Meaning transactions are mined faster [higher fees first] which allows txs with lower fees to be added on the next block sooner.
Consider the difficulty epoch to be a "period" of difficulty. So one of the 2016 block timeframes that make up a diff adjustment. The other one not sure. The points are somewhat accurate but also misleading. If there is a prolonged downturn in BTC price, clearly there will be some Farms that can't cover costs and pay the bills. This tends to balance out though as a decrease in hashrate means an increase in mining rewards.
The second one on fees , not so much. You would need to see a very large network hashrate drop to significantly impact day to day transactions. Now if it coincides with a higher than normal level of network transaction such as price swings or holidays then yes it will affect fees. No more than people FOMO'ing there transactions. I'll note here you still can choose lower fees it will just take longer to confirm.

I personally prefer the below site for monitoring network difficulty


https://diff.cryptothis.com/


░░░░░▄▄██████▄▄
░░▄████▀▀▀▀▀▀████▄
███▀░░░░░░░░░░▀█▀█
███░░░▄██████▄▄░░░██
░░░░░█████████░░░░██▌
░░░░█████████████████
░░░░█████████████████
░░░░░████████████████
███▄░░▀██████▀░░░███
█▀█▄▄░░░░░░░░░░▄███
░░▀████▄▄▄▄▄▄████▀
░░░░░▀▀██████▀▀
Ripmixer
░░░░░▄▄██████▄▄
░░▄████▀▀▀▀▀▀████▄
███▀░░░░░░░░░░▀█▀█
███░░░▄██████▄▄░░░██
░░░░░█████████░░░░██▌
░░░░█████████████████
░░░░█████████████████
░░░░░████████████████
███▄░░▀██████▀░░░███
█▀█▄▄░░░░░░░░░░▄███
░░▀████▄▄▄▄▄▄████▀
░░░░░▀▀██████▀▀
Yogee (OP)
Sr. Member
****
Offline Offline

Activity: 1540
Merit: 412



View Profile
November 23, 2020, 06:33:25 AM
 #4

There is no accurate way to ascertain the hashrate of the network as there's no data available. When you're looking at the hashrate displayed by the websites, it's usually derived from the block intervals of the blocks and the accuracy of that doesn't usually matter, so keep that in mind.
Yes, I have seen a formula about hashrate but there's also a disclaimer that there's no exact way to compute it.

Quote
Epoch simply means the period of time so difficulty epoch is the n-th difficulty period, with n being an integer which signifies the number of difficulty adjustment that has occurred. The other block time, difficult epoch is the avg block interval in the current difficulty period.

The difficulty is adjusted based on the "block interval of the current difficulty epoch" (or the past 2016 block at the point of difficulty adjustment), so it'll be more accurate to refer to that metric as compared to the avg interval of the previous 2016 block.
If I'm to use the example above, this means
- there have been 327 times that mining difficulty had been adjusted
- it takes 8 mins and 51 secs to mine a block on ave. from the 327th adjustment which is 9 mins & 18 secs. to the current block time

Quote
Having a relatively long block interval over a period of time doesn't mean that the miners have turned off their ASICs, it could just be varience affecting it.
Appreciate it if you could talk more about this variance or just link me to an article.

.................

Here is a thread I wrote a while ago that covers more the mining side of things and helps people figure out if mining is for them. Most of these statistics don't mean anything to the general BTC public, apart from th eodd long block contributing to network congestion.
First time/Small miner reference for getting started.
Thanks! Will look into this.

Quote
The points are somewhat accurate but also misleading. If there is a prolonged downturn in BTC price, clearly there will be some Farms that can't cover costs and pay the bills. This tends to balance out though as a decrease in hashrate means an increase in mining rewards.
The second one on fees , not so much. You would need to see a very large network hashrate drop to significantly impact day to day transactions. Now if it coincides with a higher than normal level of network transaction such as price swings or holidays then yes it will affect fees. No more than people FOMO'ing there transactions. I'll note here you still can choose lower fees it will just take longer to confirm.
Maybe worded poorly but what I'm trying to say is
- people predict that btc price will drop if hash rates drop
- a prolonged congested mempool forces more people to pay higher fees if they want their transactions to be confirmed quickly. If the blocks are mined faster due to increase in hash rates and difficulty yet to be adjusted, txs with highers fees are cleared sooner than expected until all that's left are txs with lower fees. I'm assuming nobody else is crazy enough to put 100 sats/vbyte if the current highest priority is 10 sats/vbyte.

Quote
I personally prefer the below site for monitoring network difficulty
https://diff.cryptothis.com/
The "presale" was a turn off but bookmarked anyway.

R


▀▀▀▀▀▀▀██████▄▄
████████████████
▀▀▀▀█████▀▀▀█████
████████▌███▐████
▄▄▄▄█████▄▄▄█████
████████████████
▄▄▄▄▄▄▄██████▀▀
LLBIT|
4,000+ GAMES
███████████████████
██████████▀▄▀▀▀████
████████▀▄▀██░░░███
██████▀▄███▄▀█▄▄▄██
███▀▀▀▀▀▀█▀▀▀▀▀▀███
██░░░░░░░░█░░░░░░██
██▄░░░░░░░█░░░░░▄██
███▄░░░░▄█▄▄▄▄▄████
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
█████████
▀████████
░░▀██████
░░░░▀████
░░░░░░███
▄░░░░░███
▀█▄▄▄████
░░▀▀█████
▀▀▀▀▀▀▀▀▀
█████████
░░░▀▀████
██▄▄▀░███
█░░█▄░░██
░████▀▀██
█░░█▀░░██
██▀▀▄░███
░░░▄▄████
▀▀▀▀▀▀▀▀▀
|
██░░░░░░░░░░░░░░░░░░░░░░██
▀█▄░▄▄░░░░░░░░░░░░▄▄░▄█▀
▄▄███░░░░░░░░░░░░░░███▄▄
▀░▀▄▀▄░░░░░▄▄░░░░░▄▀▄▀░▀
▄▄▄▄▄▀▀▄▄▀▀▄▄▄▄▄
█░▄▄▄██████▄▄▄░█
█░▀▀████████▀▀░█
█░█▀▄▄▄▄▄▄▄▄██░█
█░█▀████████░█
█░█░██████░█
▀▄▀▄███▀▄▀
▄▀▄
▀▄▄▄▄▀▄▀▄
██▀░░░░░░░░▀██
||.
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
░▀▄░▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄░▄▀
███▀▄▀█████████████████▀▄▀
█████▀▄░▄▄▄▄▄███░▄▄▄▄▄▄▀
███████▀▄▀██████░█▄▄▄▄▄▄▄▄
█████████▀▄▄░███▄▄▄▄▄▄░▄▀
███████████░███████▀▄▀
███████████░██▀▄▄▄▄▀
███████████░▀▄▀
████████████▄▀
███████████
▄▄███████▄▄
▄████▀▀▀▀▀▀▀████▄
▄███▀▄▄███████▄▄▀███▄
▄██▀▄█▀▀▀█████▀▀▀█▄▀██▄
▄██▄██████▀████░███▄██▄
███░████████▀██░████░███
███░████░█▄████▀░████░███
███░████░███▄████████░███
▀██▄▀███░█████▄█████▀▄██▀
▀██▄▀█▄▄▄██████▄██▀▄██▀
▀███▄▀▀███████▀▀▄███▀
▀████▄▄▄▄▄▄▄████▀
▀▀███████▀▀
OFFICIAL PARTNERSHIP
FAZE CLAN
SSC NAPOLI
|
ranochigo
Legendary
*
Offline Offline

Activity: 2954
Merit: 4165


View Profile
November 23, 2020, 08:00:19 AM
 #5

Having a relatively long block interval over a period of time doesn't mean that the miners have turned off their ASICs, it could just be varience affecting it.
Appreciate it if you could talk more about this variance or just link me to an article.
Well, its a little fraction of statistics that I've learned.

The distribution of the blocks within a specific period of time follows a Poisson Distribution, which is basically a Binomial Distribution (Fixed probability and a Fixed number of trials) but with Poisson, it assumes an infinite sample. It satisfies a Poisson distribution as each of the attempt is independent of each other and that each occur with a similar probability. As such, with a given hashrate and a constant difficulty, you'll tend to have excessively small block time and excessively fast block time. However, the mean of the Poisson sample is still 10 minutes.

Thus, when you see that there's no block for an extended period of time, chances are it's due to varience. If you're looking at an extended period of extended interval (ie. 20minutes for an entire day), the probability of it being due to the varience and not miners deciding to shift their hashpower away decreases. This is why Bitcoin's difficulty adjustment has to follow a 2 weeks sample, it doesn't have any mechanism that accounts for the varience and just assumes that the varience is eliminated with a very large sampling.


*Disclaimer, I'm not a mathematician nor did I study Poisson extensively, I've only done Binomial mainly for my studies.

.
.HUGE.
▄██████████▄▄
▄█████████████████▄
▄█████████████████████▄
▄███████████████████████▄
▄█████████████████████████▄
███████▌██▌▐██▐██▐████▄███
████▐██▐████▌██▌██▌██▌██
█████▀███▀███▀▐██▐██▐█████

▀█████████████████████████▀

▀███████████████████████▀

▀█████████████████████▀

▀█████████████████▀

▀██████████▀▀
█▀▀▀▀











█▄▄▄▄
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
.
CASINSPORTSBOOK
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄
▀▀▀▀█











▄▄▄▄█
MusaMohamed
Sr. Member
****
Offline Offline

Activity: 896
Merit: 290



View Profile
November 24, 2020, 01:23:27 AM
Last edit: November 24, 2020, 01:36:28 AM by MusaMohamed
 #6

The distribution of the blocks within a specific period of time follows a Poisson Distribution, which is basically a Binomial Distribution (Fixed probability and a Fixed number of trials) but with Poisson, it assumes an infinite sample. It satisfies a Poisson distribution as each of the attempt is independent of each other and that each occur with a similar probability. As such, with a given hashrate and a constant difficulty, you'll tend to have excessively small block time and excessively fast block time. However, the mean of the Poisson sample is still 10 minutes.
Bitcoin Wiki (Confirmation). It says the bitcoin block interval follows the Poisson distributions and it is correct with the Bitcoin block confirmations. Investopedia has an article for Poisson distribution: Poisson Distribution (Investopedia). It is for count data that is bitcoin block data has.


Quote
Key Takeaways

- A Poisson distribution is a measure of how many times an event is likely to occur within "X" period of time.
- Example: A video store averages 400 customers every Friday night. What is the probability that 600 customers will come in on any given Friday night?
- It was named after mathematician Siméon Denis Poisson.

R


▀▀▀▀▀▀▀██████▄▄
████████████████
▀▀▀▀█████▀▀▀█████
████████▌███▐████
▄▄▄▄█████▄▄▄█████
████████████████
▄▄▄▄▄▄▄██████▀▀
LLBITCRYPTO
FUTURES
[
1,000x
LEVERAGE
][
.
COMPETITIVE
FEES
][
INSTANT
EXECUTION
]██████
██
██
██
██
██
██
██
██
██
██
██
██████
████████████████████████████████████████████████████████
.
TRADE NOW
.
████████████████████████████████████████████████████████
██████
██
██
██
██
██
██
██
██
██
██
██
██████
CryptocurencyKing
Hero Member
*****
Offline Offline

Activity: 1288
Merit: 504


View Profile
November 24, 2020, 08:57:16 AM
 #7

To be sincere with you, this amongst others that deals with coding and other technicalities are the most difficult subjects to understand in this forum and should rather be treated very delicately as, a disconnection from the flow of knowledge don't only end at that point but, confuses you up to the previously understood concepts.
That's how dangerous calculations that deals with the integration of already laid down concept could be and while explaining this concepts, doing so along with it's relevances would help it make more meaning to whom the message is intended.
And notably, it's always confusing to use a term being defined about in the same sentence your using to explain the term. More confusion can build from there, improvision can solve this. I really need to know this.
Pages: [1]
  Print  
 
Jump to:  

Powered by MySQL Powered by PHP Powered by SMF 1.1.19 | SMF © 2006-2009, Simple Machines Valid XHTML 1.0! Valid CSS!