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The key here is "build up over time". A single electron can't provide an interference pattern because, unlike a wave, it is indivisible. What we actually detect, whether electrons or photons, is individual particles hitting the detector with a spatial distribution that looks like wave interference.
I SOLVED DOUBLE SLIT SECRET !!!1 Electron is moving 2 EM wave is hiting electron3 We see wave on screen because ( WAVE IS FASTER ) I CAN CONFIRM MY THEORY IN LAB !!!