Author

Topic: BitCoin: is it really finite? (Read 425 times)

legendary
Activity: 2268
Merit: 18748
July 01, 2021, 02:58:50 AM
#32
Why would that block be valid? The rules are very simple; you generate a valid proof of work, you earn a specific amount as a reward plus the fees. It shouldn't be accepted by the network whether he generated lower or exceeded the 5 billion satoshis.
That's not what the rules state though. They state that you cannot earn above a specific amount, which is currently 6.25 BTC. The rules place no lower limit on what the miner can earn.

The actual constraint is that the sum of all the outputs in a block must be less than or equal to the sum of all the inputs in a block plus the block reward. This means a miner can never generate more than (currently) 6.25 BTC per block, but there is nothing stopping them from generating less than that.
legendary
Activity: 1512
Merit: 7340
Farewell, Leo
July 01, 2021, 01:48:52 AM
#31
One example is block 124,724, where the miner claimed a reward of 49.99999999 BTC instead of 50 BTC and also failed to claim the 0.01 BTC in fees, permanently destroying 0.01000001 BTC.
Why would that block be valid? The rules are very simple; you generate a valid proof of work, you earn a specific amount as a reward plus the fees. It shouldn't be accepted by the network whether he generated lower or exceeded the 5 billion satoshis. Conversely, everyone have the right to burn their coins, I guess that's why the developers allowed that.

But, that would be the only reason I can think of.
legendary
Activity: 2688
Merit: 1192
June 28, 2021, 02:51:10 PM
#30
Hello all,

I am new to this forum, so I hope you will not take my question wrongly.

I have been discussing Bitcoin with friends and people who have some substantial amounts.

I hear the claim that Bitcoin is finite, with a total of 21 million over and over again. However, this all seems like mind games to me and the people involved are not realising that in actual fact Bitcoin is infinite (or at least it's supply is!).


I'm not sure how exactly this is distinct to Bitcoin, it always applies to any other cryptocurrency or any currency that can be represented within a digital form. Comparing it to a water molecule is a bit silly as it is not traded like an asset in the same way and pointless as an example really. You could compare it to gold, which can have a digital representation of the value behind it and that could also be broken down to however many decimal places you wanted. The fact is people like their money have traditionally and for a very long time been used to having their money represented in large whole numbers - it doesn't sound very appealing to say I am the proud owner of 0.000001 Bitcoin, which is the direction you seem to be heading.
jr. member
Activity: 89
Merit: 4
June 28, 2021, 02:11:52 PM
#29
First  bitcoin rewards will stop at 21000000

This is not a rule, but part of the rules that make bitcoin, the fact that halving exist and the fact that minimum amount of bitcoin is 0.00000001 lead to that 21000000 coins.

Someone could say its not finite (or its not finite in a way that matters) because the coin will only reach the limit at the future, and they would be PARTIALLY right.

While the coin will only only reach its limit at far future, when people talk about bitcoin limit they are comparing with state inflation methods.

Talking about the state, they believe at doing enought monetary inflation to make sure they can be 100% sure price inflation will occur.
With bitcoin you can't be sure about that since its decided by a program at a fixed rate (not based at transaction fees, harsh rate or anything that could be used to try to maybe calculate price inflation), more after the first 4 years half of the coins were already mined, and then after more 4 years, 75% of the coins were mined..... This inflation amount is low enough and wont cause by itself, price inflation.

One can say that while it wont cause bit itself price inflation it will help to make it happen. The thing is, its obviously possible to have price inflation without monetary inflation, nxt dont have monetary inflation (and because of lost coins will even have monetary deflation), yet price deflation exist, so dont think you will evade price inflation by making the coin premined after X years.
PS:If you want a monetary inflation smaller then 2% per year (the amount of price inflation per year the state want), instead of halving you would need to EACH YEAR divide the block reward by 50, instead of dividing it by 2 every 4th years, or divide it by 12.5 every 4 years (but the less than 2% monetary inflation will happen only after start of year 6).

Also even if bitcoin is changed to allow a value smaller than 0.00000001 bitcoins, those small amount of bitcoins would be small compared to the rest of it and wouldnt matter for those who hate price inflation.
jr. member
Activity: 113
Merit: 1
June 16, 2021, 07:38:47 AM
#28
Now we have about 18000k Bitcoin. In future, year 2140,we will have 21000k bitcoin. If you have one,that means you have 1 of 21000k wealth of the world. Because he eating company ct earth and Et. This is our plan. Your wealth will adding everyday. Don't sell it. Don't play it .Remember.
member
Activity: 868
Merit: 38
Join hands and help me to grow everybody...
June 12, 2021, 03:02:46 PM
#27
You stated your findings very well and well articulated, but I didn't get you. I tried my best to compare your water molecules analogy,  I read and read bur I didn't understand. However, I have always have it in mind that BTC is no finite but I cannot prove it. Maybe I will get to understand you first and research more
legendary
Activity: 2268
Merit: 18748
June 12, 2021, 07:15:38 AM
#26
Sir, from which channels did you get these news? News、data on the chain or something else?
You can get all this data simply from examining the blockchain.

If you aren't running your own node, then the easiest way of searching blockchain data that I have found is via blockchair.com. For example, take a look at this customized search link - https://blockchair.com/bitcoin/blocks?q=reward(5000000000),fee_total(1..)#

This link shows all the blocks in which the miner claimed a reward of exactly 50 BTC, but which also included at least 1 satoshi in fees. Since the miner only claimed the exact 50 BTC block reward, then all the fees from these blocks - some 194 blocks, totallng 9.66234623 BTC - are permanently lost.
member
Activity: 98
Merit: 173
June 12, 2021, 06:56:43 AM
#25
When did the miners fail to claim the reward?
One example is block 124,724, where the miner claimed a reward of 49.99999999 BTC instead of 50 BTC and also failed to claim the 0.01 BTC in fees, permanently destroying 0.01000001 BTC.

A more notable example is block 501,726, where the miner failed to claim the entire reward of 12.5 BTC.

Block 526,519 only claimed 6.25 BTC instead of the maximum 12.5 BTC permitted.

Block 162,705 failed to claim any of the fees in the block, only claiming the 50 BTC block reward, resulting in a loss of 0.0240192 BTC.

There are lots more examples of miners making similar mistakes.
Sir, from which channels did you get these news? News、data on the chain or something else?
By the way, I read your other replies, you are very knowledgeable and proficient in Bitcoin, which makes me not surprised at your 6000+ merit.
legendary
Activity: 2268
Merit: 18748
June 12, 2021, 04:22:25 AM
#24
When did the miners fail to claim the reward?
One example is block 124,724, where the miner claimed a reward of 49.99999999 BTC instead of 50 BTC and also failed to claim the 0.01 BTC in fees, permanently destroying 0.01000001 BTC.

A more notable example is block 501,726, where the miner failed to claim the entire reward of 12.5 BTC.

Block 526,591 only claimed 6.25 BTC instead of the maximum 12.5 BTC permitted.

Block 162,705 failed to claim any of the fees in the block, only claiming the 50 BTC block reward, resulting in a loss of 0.0240192 BTC.

There are lots more examples of miners making similar mistakes.
legendary
Activity: 3472
Merit: 10611
June 12, 2021, 03:52:17 AM
#23
When did the miners fail to claim the reward? You mean that they chose to enter a burning address as the one rewarded?
When the miner constructs the coinbase transaction they can set the amount to anything <= (reward + fees) for example if they set it to 5 they lose 1.25 + fees. I know of one occasion when the user set their amount to 50 (in early days) and forgot to add the fees, obviously this was modified software and the user made the mistake.

Quote
I still don't understand why Satoshi chose to be rewarded with 50 non spendable bitcoins.
Because block 0 (ie. Genesis block) was mined before the software was released which makes those coins premined. I don't know if this was actually the intention but if those coins were included in spendable UTXOs it would have been considered unfair. That goes against bitcoin's principles.
legendary
Activity: 1512
Merit: 7340
Farewell, Leo
June 12, 2021, 03:45:11 AM
#22
There have also been a couple of occasions in which miners have failed to claim the entire block reward they were allocated, and so these bitcoin are also permanently lost and would need to be subtracted from the total supply.
When did the miners fail to claim the reward? You mean that they chose to enter a burning address as the one rewarded?

And of course the very first 50 bitcoin mined in the genesis block can't actually be spent, so you could subtract them from the total supply as well.
Actually, those bitcoins are by default not included into circulation. We count with halvings and the genesis block isn't included into any period. The first 210,000 blocks rewarded bitcoins that can be normally spent and if you sum them all you'll get 10,500,000 BTC. I still don't understand why Satoshi chose to be rewarded with 50 non spendable bitcoins.

I think we should properly exclude only the OP_RETURN values. A study says that around 1.8 million OP_RETURN transactions have been made, but I can't find the number of bitcoins lost. It should be easy with to calculate with a bitcoind and a script.
legendary
Activity: 2268
Merit: 18748
June 12, 2021, 03:34:08 AM
#21
A key limiting factor is that the smallest unit of Bitcoin is 8 digits after the decimal point.So 1/2n must be greater than 0.00000001
This will first play a part when we hit block 2,100,000. At that point, the block reward will drop from 0.09765625 BTC to 0.04882812 BTC, meaning we will lose 0.5 sats from every block mined.

Because of these accumulated rounding errors, the total number of bitcoin which could ever be mined is actually 20,999,999.9769. There have also been a couple of occasions in which miners have failed to claim the entire block reward they were allocated, and so these bitcoin are also permanently lost and would need to be subtracted from the total supply. And of course the very first 50 bitcoin mined in the genesis block can't actually be spent, so you could subtract them from the total supply as well.
member
Activity: 98
Merit: 173
June 12, 2021, 03:05:51 AM
#20
This is the case for the first four years:365*24*6*25*4=10512000 btc
If you want to be precise, that's wrong, because within 4 years, there's a 29th of February. I don't know why you want to calculate it that way, but it'd be like this for the first halving: 50*144*x = 10500000 => x = 4375/3 = 1,458.3 days.
Even better: "years" have nothing to do with it, Bitcoin halvings happen every 210,000 blocks.

It seems OP left Bitcointalk 14 minutes after he created his account. Maybe he's learning math, maybe he's still adding nines to 0.999999999999999999999 to proof it's infinite and will become larger than 1 if he is persistent enough.
yes,it's right.

I edited my reply:Sorry i made a few small mistakes.
This is the case for the first four years:In fact, the time is calculated based on 210,000 blocks, each block is 10 minutes,
so it should be 210000*10/60/24=1458.333..days
The number of bitcoins you get in first 1458.33..days is 210,000*50=10500000
Since it is halved every 1458.33..days , you can use the following formula to calculate:10500000*(1+1/2+1/22+.....+1/2n)
legendary
Activity: 3290
Merit: 16489
Thick-Skinned Gang Leader and Golden Feather 2021
June 12, 2021, 02:40:40 AM
#19
This is the case for the first four years:365*24*6*25*4=10512000 btc
If you want to be precise, that's wrong, because within 4 years, there's a 29th of February. I don't know why you want to calculate it that way, but it'd be like this for the first halving: 50*144*x = 10500000 => x = 4375/3 = 1,458.3 days.
Even better: "years" have nothing to do with it, Bitcoin halvings happen every 210,000 blocks.

It seems OP left Bitcointalk 14 minutes after he created his account. Maybe he's learning math, maybe he's still adding nines to 0.999999999999999999999 to proof it's infinite and will become larger than 1 if he is persistent enough.
member
Activity: 98
Merit: 173
June 12, 2021, 02:20:14 AM
#18
This is the case for the first four years:365*24*6*25*4=10512000 btc
If you want to be precise, that's wrong, because within 4 years, there's a 29th of February. I don't know why you want to calculate it that way, but it'd be like this for the first halving: 50*144*x = 10500000 => x 4375/3 = 1,458.3 days.

Since it is halved every four years, you can use the following formula to calculate:10512000*(1+1/2+1/22+.....+1/2n)=21000000btc
Yes, you can. In the 34th halving the reward won't be greater than 0.00000001.
lol, yes, thank you for your reminder, for the convenience of calculation,I did not consider this particular situation.
legendary
Activity: 1512
Merit: 7340
Farewell, Leo
June 12, 2021, 02:05:03 AM
#17
This is the case for the first four years:365*24*6*25*4=10512000 btc
If you want to be precise, that's wrong, because within 4 years, there's a 29th of February. I don't know why you want to calculate it that way, but it'd be like this for the first halving: 50*144*x = 10500000 => x = 4375/3 = 1,458.3 days.

Since it is halved every four years, you can use the following formula to calculate:10512000*(1+1/2+1/22+.....+1/2n)=21000000btc
Yes, you can. In the 34th halving the reward won't be greater than 0.00000001.
member
Activity: 98
Merit: 173
June 12, 2021, 01:28:22 AM
#16
I want to share my views as a novice.

One block every ten minutes will be rewarded at the beginning of the packaged 50 bitcoins.
Four years later, each package will be rewarded with 25 bitcoins.
After four years, it will be 12.5, which means it will be reduced by half every four years.
Let’s first calculate how many bitcoins there are.First, you will calculate a block every ten minutes. One block has a reward of 50 bitcoins, an hour and 60 minutes, 6 times of calculating opportunities, 24 hours a day, 365 days a year.


This is the case for the first four years:365*24*6*50*4=10512000 btc

Since it is halved every four years, you can use the following formula to calculate:10512000*(1+1/2+1/22+.....+1/2n)=21000000btc

(A key limiting factor is that the smallest unit of Bitcoin is 8 digits after the decimal point.So 1/2n must be greater than 0.00000001)

edit:Sorry i made a few small mistakes.
This is the case for the first four years:In fact, the time is calculated based on 210,000 blocks, each block is 10 minutes,
so it should be 210000*10/60/24=1458.333..days
The number of bitcoins you get in first 1458.33..days is 210,000*50=10500000
Since it is halved every 1458.33..days , you can use the following formula to calculate:10500000*(1+1/2+1/22+.....+1/2n

legendary
Activity: 2310
Merit: 4085
Farewell o_e_l_e_o
June 07, 2021, 07:26:06 AM
#15
Why is Bitcoin’s supply limit set to 21 million?
Or just look at the graph:
...
Obviously it won't ever cross (or even reach) 21 million.
A different chart from Bitcoin Wiki - Controlled supply and a different visual presentation from @fillippone with Equivalent Network Time
👉 Bitcoin will become more precious with time and with more amount of lost Bitcoin.
legendary
Activity: 3668
Merit: 6382
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June 07, 2021, 04:33:46 AM
#14
Satoshi even touched on the possibility of adding more decimals or even moving the decimal point to make the numbers easier to deal with:

I didn't know that. Thank you.
However, it doesn't change that such change will allow... some... have more ammo to claim that this is not the original Bitcoin (hence my use for the word  "arguably").
legendary
Activity: 2268
Merit: 18748
June 07, 2021, 04:28:52 AM
#13
changes which arguably will make it not be the "original bitcoin" anymore (!)
I don't think that's true. We have made plenty of changes to the original bitcoin code, and yet what we have is still the only true bitcoin. Satoshi even touched on the possibility of adding more decimals or even moving the decimal point to make the numbers easier to deal with:

Eventually at most only 21 million coins for 6.8 billion people in the world if it really gets huge.

But don't worry, there are another 6 decimal places that aren't shown, for a total of 8 decimal places internally.  It shows 1.00 but internally it's 1.00000000.  If there's massive deflation in the future, the software could show more decimal places.

If it gets tiresome working with small numbers, we could change where the display shows the decimal point.  Same amount of money, just different convention for where the ","'s and "."'s go.  e.g. moving the decimal place 3 places would mean if you had 1.00000 before, now it shows it as 1,000.00.

And as Satoshi says, relevant to OP's question, regardless of how many decimal places you use, or even where you put the decimal point, it is always the "same amount of money".
legendary
Activity: 3668
Merit: 6382
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June 07, 2021, 03:39:57 AM
#12
Therefore, 21 Million litres of Water actually has a limit, both in TOTAL and in DIVISIONS and is therefore a FINITE resource.

First of all, while 21M litres of water you can also split into very very small droplets (of water), it's still 21m litres.
Then, while 21M litres of water you can split into much more very small droplets, with Bitcoin you cannot do the same just like that.

Now, Bitcoin. Indeed, the 21M Bitcoin you can see as 2 100 000 000 000 000 satoshi, but that's still 21M bitcoin.
Now, the problem is that without changes deep in the code, changes which arguably will make it not be the "original bitcoin" anymore (!), we cannot go (on bitcoin blockchain) "deeper" than the satoshi unit, while with water you can go as low as the H2O molecule (much lower than the visible droplet).
legendary
Activity: 3472
Merit: 10611
June 06, 2021, 11:00:21 PM
#11
I think this is the wrong argument to make here. Even if it would require a hard fork, such a hard fork is not impossible. If in 100 years bitcoin is being used around the world and is worth $10 million per coin, then we can't have the scenario of the smallest spendable amount being ~$20, and so a hard fork to add more decimals may well take place. Further, Lightning network already goes to 11 decimal places and milli-satoshi, so already provides a 1000x increase in divisibility over the main chain. However, neither of these things change the fact that there a finite number of bitcoin which can ever exist.
Well OP wasn't arguing about what may or may not happen in the future but what is true right now (which obviously is false).
As for Lightning Network, what the second layer does is not going to change the bitcoin protocol. So bitcoin is still not divisible to any smaller units than a satoshi. Another second layer could give you 1 bitcoin for every 2 bitcoin you lock in a channel and that still wouldn't change anything about bitcoin protocol.
legendary
Activity: 1512
Merit: 7340
Farewell, Leo
June 06, 2021, 09:35:23 AM
#10
I am new to this forum
Welcome.

The Bitcoin TOTAL is indeed fixed at 21 million. OK, that makes it finite right? Very Wrong!
No, that makes you very wrong, because you're comparing finiteness with divisibility. If you pictured bitcoins as actual coins, there wouldn't be more than 21 million, which makes the supply limited. It doesn't matter if in the next decade we propose the Nakamotos (= 0.001 sats); Bitcoins will remain the same.

You should think about it. If gold could be caught in infinite pieces, would it make my gram infinite?
legendary
Activity: 2702
Merit: 3045
Top Crypto Casino
June 06, 2021, 09:27:45 AM
#9
The smallest unit in bitcoin is Satoshi and if the need to add more decimals arises then we will be simply creating a smaller unit but this doesn't make the bitcoin supply infinite.
Take the lightning network as an example. It allows sending fractions of Satoshis but this does not change the total supply of bitcoins.

If we want the supply to become infinite then we should remove the block reward halving rule as it's it what ensures we can't mine more than 21 million btc.
legendary
Activity: 3290
Merit: 16489
Thick-Skinned Gang Leader and Golden Feather 2021
June 06, 2021, 03:31:42 AM
#8
What would you make of this?
You're making a fundamental mistake: Bitcoin is based on math, while your comparison reminds me of ancient philosophy:
Quote
In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
    — as recounted by Aristotle, Physics VI:9, 239b15

Or just look at the graph:
Image loading...
Obviously it won't ever cross (or even reach) 21 million.
legendary
Activity: 2268
Merit: 18748
June 06, 2021, 02:52:07 AM
#7
No it is not. To divide the smallest unit (1 Satoshi) into smaller parts you would have to change the consensus rules using a hard fork.
I think this is the wrong argument to make here. Even if it would require a hard fork, such a hard fork is not impossible. If in 100 years bitcoin is being used around the world and is worth $10 million per coin, then we can't have the scenario of the smallest spendable amount being ~$20, and so a hard fork to add more decimals may well take place. Further, Lightning network already goes to 11 decimal places and milli-satoshi, so already provides a 1000x increase in divisibility over the main chain. However, neither of these things change the fact that there a finite number of bitcoin which can ever exist.

If doesn't matter how much you divide up 21 million, there will still only ever be (slightly fewer than) 21 million bitcoin. There are infinite numbers between 0 and 1. That doesn't make 1 = infinity.

As for OP's water analogy, given the molecular weight of water is 18, in one liter of water there are 3.35*1025 molecules. To apply the same degree of divisibility to bitcoin, the smallest unit would be somewhere around 0.00000000000000000000000001, or one milli-milli-milli-milli-milli-milli-satoshi. If that was equivalent to 1 US cent, a single bitcoin would be worth 1 trillion trillion dollars.
legendary
Activity: 1512
Merit: 4795
Leading Crypto Sports Betting & Casino Platform
June 05, 2021, 11:09:04 PM
#6
<...>
Finite is a supply people can achieve over a certain time period. Like gold as an example, no gold miner or any other person can predict when all gold will be mined, even if estimated, it will take millions or billions of yeras, this makes gold infinite, unlike Bitcoin that almost 19 million are mined already. The total Bitcoin supply is 21 million in which over 98% would have been mined by 2050, this makes the supply finite. What some people argue is that the Bitcoin community can agree one day to increase the supply, but this can not happen because people would even prefer if the supply is reduced which will help in Bitcoin price valuation.
legendary
Activity: 3472
Merit: 10611
June 05, 2021, 10:33:11 PM
#5
The thing is Bitcoin is infinitely divisible, it can go as small as it needs to go, you can own 0.1% or 0.0000000000001% or even less...
No it is not. To divide the smallest unit (1 Satoshi) into smaller parts you would have to change the consensus rules using a hard fork.
In simple terms you can send 0 satoshi, you can send 1 satoshi but you can't send 0.1 or 1.1 satoshis.

By strict rules the amount field of each transaction is of a 64-bit integer type and the values it can contain is between 0 and 2100000000000000 (21 million bitcoin in satoshis). If you want to divide this to smaller values you'll have to first convince the entire bitcoin network to accept a hard fork where it changes this field into another integer type that supports smaller units and allows values outside of the mentioned range.

Not to mention that in math 1 = 1.0 = 1.00 = 1.000 = ...

P.S. It is "bitcoin" not "BitCoin".
legendary
Activity: 2758
Merit: 6830
June 05, 2021, 09:36:39 PM
#4
In simple terms...

Let's imagine I have 1 BTC right now. In a few years, all 21 million BTC will be mined and I'll have 1/21,000,000 of the total BTC supply. Does that proportion change if people start saying that there are now 21,000,000,000 BTC (100x smaller unit)? Nah, I'll have 100/21,000,000,000... my share of the total BTC supply hasn't been diluted, and that's all that matters. Smiley
copper member
Activity: 2338
Merit: 4543
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June 05, 2021, 09:31:34 PM
#3
~

You're question has nothing to do with bitcoin, it's simple math.  1 is 1.  It's fixed at 1, no matter how many times you divide it, it's still 1.  1 doesn't' become worth more when you divide it, the value of the sum of it's denominations is is still 1.
legendary
Activity: 3038
Merit: 4418
Crypto Swap Exchange
June 05, 2021, 09:26:42 PM
#2
It is finite.

Bitcoin's block rewards follows a geometric progression where the rewards halves every 210,000 blocks. If you were to take the sum of the geometric progression, it would be 21 million. This means that in a scenario whereby you have infinite number of blocks, the total supply cannot exceed 21 million no matter how divisible it gets. Making something more divisible doesn't change the fact that the total supply is the same. The value of each denomination is still proportionally smaller.
newbie
Activity: 1
Merit: 0
June 05, 2021, 09:24:11 PM
#1
Hello all,

I am new to this forum, so I hope you will not take my question wrongly.

I have been discussing Bitcoin with friends and people who have some substantial amounts.

I hear the claim that Bitcoin is finite, with a total of 21 million over and over again. However, this all seems like mind games to me and the people involved are not realising that in actual fact Bitcoin is infinite (or at least it's supply is!).

Before you jump on me, please allow me to explain.

The Bitcoin TOTAL is indeed fixed at 21 million. OK, that makes it finite right? Very Wrong!

The thing is Bitcoin is infinitely divisible, it can go as small as it needs to go, you can own 0.1% or 0.0000000000001% or even less...

This means that while the TOTAL is finite, the number of denominations / fractions / divisions has no limit.

Isn't everything like that? Isn't it the TOTAL that counts? NO.... and here is where the trick lies:

Let's make a thought experiment and take 21 million Bitcoin vs 21 Million litres of Water. Are both infinitely divisible? NO!

The Bitcoin is, you simply go smaller and smaller....... but you cannot do this with water, once you reach 1 molecule of water (H20), you cannot divide it further whilst keeping it as water...... if you break up the H20 Molecule it is not water anymore.

Therefore, 21 Million litres of Water actually has a limit, both in TOTAL and in DIVISIONS and is therefore a FINITE resource.

Bitcoin on the other hand has a limit in TOTAL, but not in DIVISIONS and is therefore an INFINITE resource.

None of the people heavily involved in Bitcoin have accepted or admitted this, on the other hand people with less or no investment, especially from Scientific and economic backgrounds, have agreed with me.

What would you make of this?




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