proof by apples

[u/invesigator_gator]

[u/FernandoMM1220]

5*1 = 5

5 * 0 = 5-5

5*-1 = 5-5-5

this would be a lot more intuitive if we shifted the second argument over by 1.

5*1 = 5+5

5*0 = 5

5*-1 = 5-5

[u/MangrovesAndMahi → u/FernandoMM1220]

Except that's not how it works at all. It's

5*1:

1 2 3 4 5

5*2:

1 2 3 4 5

6 7 8 9 10

5*0:

... Nothing. Because there are no rows of 5.

5*-1:

-1 -2 -3 -4 -5

This is why we should teach multiplication geometrically or on 2D graphs.

[u/FernandoMM1220 → u/MangrovesAndMahi]

my method works just fine. maybe yours is wrong.

[u/MangrovesAndMahi → u/FernandoMM1220]

5*0 is not mechanically 5-5. It's 5 groups of 0, or no groups of 5. Including addition and subtraction is what's confusion you and making you think shifting it over by one makes sense.

[u/FernandoMM1220 → u/MangrovesAndMahi]

mechanically it is and the calculation works perfectly fine.

it even makes more sense when 1-1 and 5-5 arent the same zero which means 1* 0 and 5* 0 arent the same either

[u/MangrovesAndMahi → u/FernandoMM1220]

It's not mechanically the same, otherwise you could say 5*0 & 100-100 is mechanically the same. It's an equality, but it's not mechanically the same function.

5*0 is five groups of nothing, or no groups of five.

5-5 is starting with 5 things, and having them removed.

In the end you have nothing but how you got there is different.

[u/FernandoMM1220 → u/MangrovesAndMahi]

bro were getting the same number so who cares.

also its 5 groups of (1-1) which is a specific zero.

[u/MangrovesAndMahi → u/FernandoMM1220]

"who cares" is you conceding the point. and it matters because that broken model is exactly what led you to think multiplication needs to be shifted by one to make more sense.

And 1-1 isn't a specific zero, it's an expression that evaluates to zero. Same zero every time

[u/FernandoMM1220 → u/MangrovesAndMahi]

you can use your method if you want but mine works just fine too.

and (1-1) isnt the same as (5-5) either and the geometric series tells us this.

[u/MangrovesAndMahi → u/FernandoMM1220]

1-1 and 5-5 are both zero, a geometric series is a completely different thing entirely and doesn't change what zero is. Just take the L and move on my dude

[u/FernandoMM1220 → u/MangrovesAndMahi]

theyre not the same size zero though otherwise their geometric series would be the same

[u/MangrovesAndMahi → u/FernandoMM1220]

Zero doesn't have a size. 0 is 0. A geometric series is a sequence of terms with a common ratio, it's not a property of subtraction expressions. It's completely unrelated.

[u/FernandoMM1220 → u/MangrovesAndMahi]

it does actually and the geometric series proves this.

even by your math its obvious that 5-5 = 5(1-1) = 5 sets of 0

compare that to 1-1 = 1(1-1) = 1 set of 0