Actually none of that is true - it is pretty obvious you are blow-hard that really does not understand the subject. Compaq did not take the bios out of the machine. Compaq used two groups of software engineers - one that had access to the source code for the bios (software) and one that did not and wrote a bios (software) that functioned like the IBM bios (by observing the functioning of an IBM PC). Compaq reverse-engineer software, not hardware. The bios software is written to ROM chips - all software is written to some form of hardware.
Let's repeat the first line of the definition:
In computing, firmware is software that is embedded in a hardware device, that allows reading and executing the software, but does not allow modification, e.g., writing or deleting data by an end user.
Now will you stop trying to claim firmware<>software. The only difference between the subgroup firmware and the superset software is firmware is read-only - all software is contained on a hardware device.
Last example:
Draw circle the size of a diner plate.
That is group A
Draw a circle inside of the group A circle the size of a quarter.
That is group B
The area inside of group B is 100% group A
B=A
The area inside of group A is not 100% of group B - only a small percent of A is within group B
A<>B
Group A is software and group B is firmware.
In the first sentence, you implore him to stop saying they're different. In the second sentence, you outline a difference. LOL