Ah yes, some of my past posts, my 2 cents worth on various subjects. Was it you that I talked with in re to the 4 laws of multiplication & division? There is a quantity/quality principle of complementarity in math similar to the wave/particle duality in physics.
In other words : ONE(quantity), then ONE FINGER(quality)(which I often get in response to my inventions : the one-soldier-at-attention finger salute).
Law #1 : Multiplication is repetitive addition(quantity).
Law #2 : Multiplication is vector comparison(quality).
Law #3 : Division is repetitive subtraction(quantity).
Law #4 : Division is vector partition(quality).
Simple experiment : watermelon and sharp knife. Ask some smart A$$ed mathematician that always refers to infinity as being some THING, to cut up the watermelon into a infinite number of pieces by slicing ZERO pieces off. But stand WAY back from the knife as this magician's LIE is exposed...you'll know when his eyes start to roll in terror like a cow on its way down the chute to the slaughter house....
Thus zero and infinity are 0 and 00(figure 8 sideways)is nothing and a crosseyed nothing. By Law #3 : n/0=n-0-0-0-0-...until hell glaciates or the world wears flat...-0-0-0-... = n-0=n. That's all, rotate / 45 degrees to - and you see REALITY in a quantitative sense. Then rotate x 45 degrees to + and nx0=n+0=n.
Simple : what is 2x3x0? 6 units of magnitude, 6 unit lines, 6 areas, or 0 volumes? See, what is the VALIDITY of that zero vector in the equation? What was it you were looking for? Areas or Volumes? Thus nx0 = n or o, two perfectly valid answers as to quantity vs quality.
Thus why these nonsensical contortions of renormalization(balancing + infinities with - infinities)when with n/0=n you neatly solve the problem(Law #3 : n/0=n).
Now, how did I come by this? Reading a scientific american article on Fermat's Last Theorem(A^n+B^n not equal to C^n where n>2)many years ago, I pondered that for quite awhile(math is portable, carried around in your head). Bottom line : You have to ADD n vectors on one side to equal the vector on the other side(in diophantine whole natural numbers).
Thus 3^2+4^2=5^2, 5^2+12^2=13^2, the well known pythagorean series. Then 3^3+4^3+5^3=6^3, 1^3+6^3+8^3=9^3. Then tried the 4th power series(A^4+B^4+C^4+D^4=E^4)but there rapid divergence and mods of only 0,1,5 or 6...it didn't look too promising. Had a fellow do a computer run up to 70^4 but nothing(got a LOT of 13s though).
Then on a math website : 30^4+120^4+272^4+315^4=353^4, that was figured out by Norrie in 1910(long before computers). Imagine the PAPER calcs he must have gone thru... Now what does that have to do with 4 vector space-time? Note my "handle", it's an in joke. There is no such thing as "time" in and of itself.
So, what can we do with n/0=n=nx0 ? E=mc^2=hw where h is Planck's Constant and w is DeBroglie's wave number. Thus in a pure Momentum-line state, m=0 and h=0(as mass-area change, ie delta kinetic energy). It reduces then to E=c^2=w with n/0=n=nx0. Then DeBroglie's equation for the speed of a matter wave crest is U=c^2/v. With v=0(internally, locally)the global velocity is c^2 or 9 x 10^16 km/sec(1 light year in 105 seconds)in a pure Momentum-line state. Now you know how "they" get around the universe so fast, "they" overcame the nonsense that INFINITY is some THING. It's NOTHING dude...NO....THING....at....all....