In TeX, single $ means "change to math typesetting mode" (treat it as"inline" math). The double $$ is similar, just it typesets it as a separate block of math/figure (it adds alignment, spacing, etc.).

I'd expect similar behaviour.

It is not a theft. It is a robbery.

Sure.

This is not related to a mining lottery. Finding 3 blocks in 3 days requires quite a lot of hash power. Bitaxes, even though I like them, would not be that lucky.

I believe that both have infinite number of solutions. However, when looking into the chart of sin(x) and sin(x^2), it is quite obvious, that both the infinities have different cardinality.

I'd say that the number of solutions for cos(x)=0 has same cardinality as the set of all natural numbers. However, for the cos(x^2)=0, the cardinality would be as the set of all real numbers. At least, it is not greater.

Could you add sources?

What do you mean by ECC? There is ED25519 ECC curve recommended to be used because it is independent and does not have these issues. Thus, blaming ECC as a whole is quite inaccurate and misleading.

No paper, just in head...

Some easy facts:

1000*1000=(999+1)*(999+1)
999*1000=999,000
1000-999=1

The hard mental math:

999*(1000-1)=999,000-999=998,001

Ok, now it's obvious: (998,001-1)/998

If the hashpower really peaked at something like 90 PH then it means that the miner has available something like 268x S21 Hydro (335 TH each). Or half if we use the week average 45 PH.

This was hardly mined by bitaxe. It seems there was a miner connected to the ck solo pool with about 45 PH hashpower. That'd be more than 45000 bitaxe solo miners working together.

You can find stats at https://solostats.ckpool.org/ by using the block's coinbase address:

When I saw the pool's stat page earlier, there was reported a valid share with difficulty 102T froma miner with hashrate about 90 PH with 2 workers (pitty that I didn't make any screenshot). It has disappeared.

🤔 Meh...

Trezor?

Just don't watch the usd price and instead buy it regularly in small amounts. Bitcoin was not created to be an investment. Its goal is to become global independent money.

Bitcoin is not here to make you rich in the first place, it is here to avoid becoming poor. That's the lesson.

Before using njal.la, it's good to read this (its about domains and not VPS...): https://bulletproof-domain-abuse-guru.medium.com/whats-wrong-with-njalla-privacy-largest-review-of-bulletproof-domain-registrars-097124fa9758

The njal.la support told me they'd like to support lightning. I didn't check recently.

Really? Good to know. Their support was responsive to me. I use VPN a lot, and as well I use SSH tunnels through other servers and have never encountered any issue...

On-chain only, but you can pay more in advance.

Accepting bitcoin means "you give a BTC address to somebody while owning the appropriate private key". Every single wallet solves this issue. Maybe, you search for more privacy? Maybe you search for simple UX? What do you mean by "best"?

Being notified about received money means "I know my addresses and search for them in the blockchain". To stay private, I need my copy of blockchain on my own node. The node has documented RPC API.

The question about blacklisting sounds strange. This is a fundamental bitcoin property that transactions/addresses are very difficult to be efficiently blacklisted. Even if mining becomes more centralized, there is still high possibility for you to transact. It just might become more expensive. Moreover, there is the concept of stealth addresses.

And finally, lightning IS vanilla bitcoin as well. Maybe you wanted to say "on-chain" only bitcoin. With Bolt12, you can receive lightning bitcoin by having similar user experience as with on-chain. Anyway, it is still vanilla bitcoin.

Yes. But all physical cash today is fiat-based...

One thing is what is written in a whitepaper, maybe it's clear to me, maybe it's not, but that's not what the post was about. It was about one's perception.

For most normies I know, virtual=digital, something they believe they cannot control. That's why they prefer cash and do not care about it is fiat. Bitcoin does not look like the cash they know, thus they reject it.