I did a lot of research on this at one point, and these are what I ended up going with and was quite pleased. You can probably find them cheaper at abe books or somewhere, I'm just linking amazon for the ease (hopefully amazon links are allowed)

https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/091409...

https://www.amazon.com/Combined-Answer-Calculus-Fourth-Editi...

I have the exact same thing happen to me. I'll talk to someone from a diff area code that I never get robo calls from, and then bam, robo calls from that area code.

I'm on Verizon

looks like there are more digits cropped out so it's going to make it a lot harder since you won't know which bits you have

> The solution to a puzzle is meaningless if the same solution can be shown as the result of two different inputs.

This isn't true. There are an infinite number of inputs that result in the same solution for bitcoin (or any hash)

Right, but that's a little unfair? SHA-256 is literally a function designed to make it impossible to find such collisions. BIONIC problems aren't designed with that in mind.

Okay let’s see an example. ;)

Like it or not they are technically correct. SHA-256 is a one way compression and furthermore the PoW for bitcoin doesn't require a match for the entire hash.

There's loads of examples of this in the bitcoin network whenever there's been a fork and eventually orphaned blocks.

Those are different solutions to the puzzle. Nobody has ever published a sha-256 hash collision. It has happened once with sha-1.

The principles are the same — it's just harder to find collisions for larger digest sizes. (Although bugs in sha-1 add an interesting wrinkle to the discussion.)

In fact one could argue that encryption without requiring infinite bandwidth or computation requires finite difficulty in math puzzles.

So our current approach to encryption is fundamentally vulnerable to (vastly) more powerful adversary computers. Only things like quantum cryptography break free of that limitation, by changing the ground rules.

Algorithmic cryptography depends on a computation time approaching infinity for perfect security. Quantum cryptography depends on a data transmission rate approaching zero for perfect security. Either way, perfect security takes forever.

its not blacklist and whitelist because "black=bad, white=good", black is the abscense of light, hence the light is blocked, white would obviously be the opposite. So its black because you are blocking things, and white because you aren't.