Interesting question to consider. There are two parts to this. Firstly, 0.499999... is equal to 0.5. Thus, the answer to your question must be the same as what your answer would be if you had written 0.5. Now, *there is no nearest integer to 0.5*. - ThreadSky

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ahosbaldestin.bsky.social • 15 days ago

Interesting question to consider. There are two parts to this. Firstly, 0.499999... is equal to 0.5. Thus, the answer to your question must be the same as what your answer would be if you had written 0.5.
Now, *there is no nearest integer to 0.5*.

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ahosbaldestin.bsky.social•15 days ago

A sign of mathematical maturity is to realise that not all questions have answers, e.g., what is the largest number? e.g., what is the smallest positive real number?

ahosbaldestin.bsky.social•15 days ago

This case is a bit different to those two in that we can *adopt a convention*. We can choose our convention be either 'round up' or 'round down.'

ahosbaldestin.bsky.social•15 days ago

We may use different conventions in different circumstances. e.g., weighing yourself, e.g., marking an assignment, or so that computer programs/spreadsheets etc. don't throw out errors.

ahosbaldestin.bsky.social•15 days ago

Of course, going back to the problem as originally stated, the temptation is to say 0 because of the 4 at the start of the decimal expansion, but that would betray a lack of understanding.

truenorthbear.ca•15 days ago

In what universe is 0.49999999=0.5? It is close to 0.5. It is almost 0.5. But it is not equal to 0.5.

Would you say $49,999,999 is equal to $50,000,000? No rational person would. Sure it's only $1 off. But it is not equal. Your first point is logically, mathematically, and
demonstrably wrong.

ahosbaldestin.bsky.social•14 days ago

In no universe is 0.49999999 equal to 0.5. However the conversation is about 0.49999999..., with the ellipsis meaning that the 9 is repeated indefinitely.

truenorthbear.ca•14 days ago

Even if it goes to infinity, it's still not 0.5. No matter how you frame the conversation, 0.49999999... to infinity is still never going to equal 0.5. But if you want to believe it so bad, who am I to stand between someone and their delusions? Go off.

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