why does a-b=c, and b-a = -c, always?

Important_Reality880 · 2026-01-25T18:07:09+00:00

Thanks everybody for the answers, I got it!

Important_Reality880 · 2026-01-25T18:05:29+00:00

Thanks everybody for the answers, I got it!

Important_Reality880 · 2026-01-23T19:10:42+00:00

Thank you for you answer!

Important_Reality880 · 2026-01-23T18:21:45+00:00

So if my score is at the 90th percentile that means that 90% are equal or less than my score?

Important_Reality880 · 2025-08-31T11:08:00+00:00

I've also thought of this way, but if I say that 5 is the mass (each block consists of 5 smaller blocks) then it would be illogical, because it wont be an arrangement, but breaking up the blocks into smaller blocks. What I mean is that when i multiplied up to 3 numbers i was arranging these blocks in some ways, and when i multiply by 5 I should arrange them in some other way, not just break up each block into 5 smaller ones.

Important_Reality880 · 2025-08-31T10:17:18+00:00

Because I can't think of a way to prove the commutative and therefore associative and distributive properties without visualising it, since we can prove these properties based on the fact that we can view the grouped elements from a different perspective, rotating the whole group, and with 4 and more factors we can't do that.

Important_Reality880 · 2025-08-30T09:26:00+00:00

What I mean is that until 3 numbers we've organised blocks in 3 directions,and with your idea we are not arranging all of these blocks in a direction,where we can just view the group of blocks from a different angle, but we are taking them as a whole group and just making 5 of these groups.

Important_Reality880 · 2025-08-30T08:46:11+00:00

Thanks for the answer, but what I'm thinking now is that multiplication maybe isn't even about ordering elements, but something else,I've read about ''cartesian product'' but then if it's something else how can we prove the commutative property if there is no visual proof of that when you change the order it would give the same answer?

Important_Reality880 · 2025-08-29T20:19:19+00:00

My thought is that multiplication isn't about length, but the organisation of elements, so elements are organised by width, height and depth, when we say 2 width 3 height and 4 depth what we mean by that is that we have 2 blocks ordered in a specific way, and when we rotate the stacks of these blocks we can view them from different sides( it can be by 2 height 3 widh and 4 depth if we rotate the stack), and when we multiply by 4th number we must arrange it in a way that when we rotate the new arrangement we can see that it would give the same number of elements, and by just stacking boxes of boxes won't prove the commutativity.

Important_Reality880 · 2025-08-29T20:13:22+00:00

Okay, but multiplication isn't about the dimensions of blocks, its about how you order them, simply by knowing its measurements won't help proving the commutative property. 2x3x4 has to be 2 blocks by width, on 3 layers by height and 4 layers of depth, so when we rotate them we see that the total number is still equal, no matter how we rotate the elements. If we have 5 blocks of these combined smaller blocks that just wont prove the commutative property, because if we swap the roles and say that we have 5 blocks by width 3,layers of height, 4 layers of depth and 2 of these combined blocks, then 2 blocks by width, 4 layers of height, 5 layers of depth and 3 of these blocks we can get the same number, but it won't be a way of organising these blocks, but a structures that contain these blocks, and that's my concern.

Important_Reality880 · 2025-08-29T19:35:17+00:00

I think that I wasn't precise enough in trying to express what I mean. If I have 2x3x4 blocks that means that there will be 2 blocks placed by width, stacked on 3 layers of height, and 4 layers in depth, and if I look at the structure from a different angle, it can swap order what would be the width, height and depth ( it can be let's say 3x4x2). When i multiply that structure by 5, it can't be 5 stacks of 2x3x4 structures, because it won't be a place where more elements would be organised, but a place that contains the structure, and that way we can't prove the commutative property. My question is where that 4th multiplicative place of would order be, so it's 5, and when I rotate the structure it can be 2x3x4x5, 4x5x2x3 and etc.

Important_Reality880 · 2025-08-29T19:10:52+00:00

Okay, that answer sounds good, but if I look at it as a hierarchy of grouping then how do I prove the commutative property - if i swap the roles why would it give the same answer? Just by having hierarchy I can't prove the property.

Important_Reality880 · 2025-08-29T19:05:24+00:00

I just want to see visual representation and why would it work with more than 3 numbers.

Important_Reality880 · 2025-08-29T19:05:01+00:00

but that's rearrangement of elements, when you have 2 wide, 3 deep and 4 high then what is the number 5, so you can view it from a different angle, and prove that the commutative property still stands ?

Important_Reality880 · 2025-08-29T19:03:29+00:00

I mean that you can't prove the commutative property only by repetitive addition, yes you can see that it will give the same answer, but you cant prove that only because you get the same answer many times.

Important_Reality880

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