What do you mean by conceptual aspect?
Seriously, why do you think that they wouldn't be the same, despite all these 'mathy' proofs? I'm not fishing for a 'oh... I don't know', but rather 'I believe this for reasons X Y and Z'
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You're messing with me! You're messing with me, aren't you!?
You're making fun of me, aren't you!? Aren't you!? You definitely are! I'll murder you!