3 ms·
...uses the 0.999... = 1.0... shenanigan... Why is this a shenanigan? Do you dispute that 0.9999....=1? One easy way to see this is that there are no decimal
by skh 8y ago
...uses the 0.999... = 1.0... shenanigan...
Why is this a shenanigan? Do you dispute that 0.9999....=1? One easy way to see this is that there are no decimals between 0.9999..... and 1 and thus the two numbers are the same. A property of the real number system is that between any two distinct numbers is another distinct number.
Maybe I'm missing the intent of your statement.
- joppy 8y agoThe slightly surprising incorrect statement is “each real number has a unique decimal expansion”, which is wrong since 1.00000... = 0.99999... — so when using arguments like this, you need to be careful to always only pick one of these.
- skh 8y agoI see now. Thank you.
- mcguire 8y agoInfinitesimals forever! :-)