Hungarian scientist Ferenc Miskolczi has discovered the greenhouse gas equation Arthur Milne developed in 1922 contains a serious flaw. Milne mistakenly solved the differential equation involved by assuming an infinitely thick atmosphere. Miskolczi was working for NASA at the time and NASA suppressed his report which contradicted NASA's claims.
Miskolczi resigned in protest, stating in his resignation letter, "Unfortunately my working relationship with my NASA supervisors eroded to a level that I am not able to tolerate. My idea of the freedom of science cannot coexist with the recent NASA practice of handling new climate change related scientific results."
Miskolczi rewrote the equations and the modified equations don't indicate a runaway greenhouse effect. His equations indicate a limit to any greenhouse effect. Thus even if there is a greenhouse effect it cannot do what the Rev. Al Gore claims it will do.
Research by Stephen Schwartz also challenges claims of a runaway greenhouse effect.
I haven't studied differential equations for a few decades, but I do remember that guessing at values for variables is sometimes used to solve differential equations because of their complexity. However, there are two values that should never be used, infinity and zero. These two numbers have special mathematical properties that make them unsuitable for this purpose. For example, you may remember learning that division by zero is impossible. However, there is one special case in which division by zero is possible, zero divided by zero. The test to determine if division is correct is multiplication. Zero multiplied by any other number is zero so zero divided by zero can be any number.
In the real world it might be possible to a zero amount of any commodity, but not an infinite amount. An infinitely thick atmosphere would also be infinitely massive, i.e. a super black hole. In an infinitely thick atmosphere it wouldn't make any difference what the gases were because the gravitational attraction would be so high that radiation could not escape.