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No mate. They don't have to convince consumers. That's the point. They'll never know their money is being sent using the bitcoin network just like people don't know anything about http works when they're surfing the web now. To the consumer, the infrastructure and methodology they use will be the same as it is now.
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... thus learning nothing about Bitcoin, which brings us back to
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Why and how will this transition take place? Consumers have grown to trust these payment services, not Bitcoin.
Infrastructure will be built that allows the consumer the freedom to not to have to use a gateway. Also greater awareness, confidence, etc. Do you always make everyone repeat themselves?