SciFly

Then would you agree that in binary 1.0 > 0.111... or in decimal 1.0 > 0.999...

Then you would say that our 0.111... has a completed infinity of digits. We can then expand our thought experiment a bit. Instead of writing just one line of digits, we will write a matrix of digits like this- 1st we write 0.0 0.1 Then we will expand our matrix like this 0.00 0.10 0.01 0.11 Next 0.000 0.100 0.010 0.110 0.001 0.101 0.011 0.111 And so on forever. The question I want to ask is "will every row of this matrix have an infinite number of digits?" If they do, then will a number like pi/4 be in one of those rows?

I want to explore what people here think about infinity, and if the concept of infinity has any place in science. If I were to write down a binary number 0.1 and then a moment later append a 1 to it giving 0.11 and again 0.111 and so on for an infinite number of times. Then would the number I create ever have an infinite number of digits, as an irrational number like pi, or would it always have a finite number of digits? Also, do you think that this is a question about definitions or about necessary truth?