What's the difference between ‘A increased with B’ and ’A increased with increasing B?

It seems common to assume that ‘A increasing with B’ means that B is also increasing. It sounds like the default case. Adding additional terms 'with increasing B' sounds redundant and as such unnecessary.

It makes sense if you consider a different word. ‘A increased as B rotated’ would tell you that the relationship needs explaining.

‘A increased with increased B’ should be stated as ‘A increased as B increased’. If it is good enough for A then it should be for B.

Both are different because if we change the term I.e

"A is directly proportional to B" which means A increases when B increases, simultaneously.

if we look at the second one "A increased with B", normally a person would interpret it as the first one only. but if we look at it carefully it is an incomplete information given to us.

it can either mean "A increased with decreasing B" or "A increased with increasing B" and the last one would be "A increased with constant B"

hope it helps?

It is a long-established and widespread mathematical or scientific convention to say of two variables that, if an increase in one is associated with an increase in the other, one increases with the other. "A increases with B".

As a perfect example: "For all positive integers X, X squared increases with X."

As a more understandable but less than perfect (because some people may be very tall and also unusually thin and light) example: "Weight increases with height".

It also makes sense to say "A increases as B increases". This is clear and unambiguous and does not rely on knowing the mathematical convention.

If "A increases with decreasing B" it simply means the opposite of the above. For example: "Poverty increases with decreasing income".

"A increased with increased B" simply describes what happened in the past. For example "In our last field trials, growth increased with increased nitrogen application."