What is described here (owing apples) doesn't correctly translate into the problem (-2 x -2). This is where a lot of problems can occur. Just because the concept of minus numbers has been explained by "owing" of items in one instance doesn't mean it will hold true for all instances, and a lot of people don't understand that or just haven't had it explained to them.Corum1134 said:I plain just don't get it. Such as -2 x -2 somehow makes +4. If I owe you 2 apples then owe you twice that amount how the hell do I have 4 apples? I owe you 4 apples!
You would. When you said twice that amount, that "twice" would be a 2, not a -2, so -2*2 would equal -4, meaning yes, you would now owe 4 apples.Corum1134 said:I plain just don't get it. Such as -2 x -2 somehow makes +4. If I owe you 2 apples then owe you twice that amount how the hell do I have 4 apples? I owe you 4 apples!
Personally I didn't think mathematics was truly awesome UNTILL set theory concepts started showing up (in Sweden we start pretty late though after a cathastrophic attempt to teach it in elementary school in the 70s).Generic Gamer said:...This is because SET THEORY IS NOT MATHS! Set theory is a poor method of communication, it's an incredibly convoluted method of communicating a very simple idea!...
One theory I heard is that its because things we do naturally are often dependent on maths and engineering functions (judging distances & probabilities in sport, sums for trading, engineering for walking) we essentially do maths subconciously every day and so bringing it out of the subconcious into the concious in the form of maths lessons is easy.EscChaos said:Despite being quite adept at mathematics I often wonder how we actually manage to learn math in the first place, because at some point in our lives we must all have developed some internal logical or visual mechanic for performing calculations and understanding algebra and arithmetics and even though the subject is perhaps the only one with a perfectly consistent description and definition; all knowledge is ultimately personal.
When reading about consepts such as Metric, Hilbert or Banach spaces with features such as being cauchy or complete, I think the set theory used feels very natural. It really feels like set theory provides the best means to giving good, precise and clear definitions of those consepts.Generic Gamer said:Set theory is a fantastically simple concept, if it's taught well it's actually simpler than arithmetic, it's something we do subconsciously anyway. I just think the language is convoluted.