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If we traced an infinite universe back in time towards t=0(ish) would a singularity still be formed?

Would the singularity be infinite in size? (To me it seems it would have to be) This reminds me of infinity x zero=....

Would an infinite singularity have some very unusual properties?

Also, how could an event horizon still exist if the singularity (at t=0) was spacially infinite?

John Rennie
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