The reason for this has been the recent state of the stock market. According to yahoofinance.com, the Japanese stock market and Chinese stock market are affected by American stocks. That is because we have many international companies on both sides of Asia and America. It is a good problem in many ways for most Americans.
Russia and China will have nothing to be scared of and they will immediately start to use violence to achieve their goals like the reunification of the former territories of the Soviet Union(Russia) or taking over the South China Sea.(China)
The world relies on the US army to wipeout terrorists.
World peace would be achieved when all nations come together and talk about their differences. However, powerful nations might need to act as mediators. This is where a strong America would be useful, but it doesn't have to be America, it could be any nation stable enough to maintain a healthy economy and functioning government.
America, in spite of their faults, is the only country that the world still looks to when things go wrong. Americans will send aid to countries that suffered natural disasters. The Chinese do not. America will try to keep open the oceans for free shipping. The Chinese will not. America needs to stay strong for the good of the planet.
First of all, peace and prosperity around the world is merely a pipe dream. There's a much higher chance that humanity wipes itself out before peace and prosperity is ever achieved.
Secondly, the idea that one nation could lead the rest of the world into a new mindset is hilarious, especially since the nation in question is America. Granted, it is very big and quite influential but really, they'd need to achieve "peace and prosperity" on their own turf before they started trying to make others follow their ideals.
Thirdly, there are other powerful nations that would most probably oppose America's ideals (Russia or China maybe) or even refuse outright just because they're America (North Korea springs to mind haha).
Peace and prosperity world wide does not directly depend America. There are some countries now that are enjoying quiet existences quite far from the public eye. America can not support the entire world and the world does not want to be supported by America. Peace and prosperity is something brought about by individuals, not governments.
Prosperity around the world seems to depend on the American economy, but peace does not. America has always been strong, but that has never resulted in peace around the world. That requires all nations willing to resolve disputes, without violent conflict. It is unlikely to ever happen, and certainly not something America can do alone.
No, I disagree that peace and prosperity around the world depend on a strong America, because lots of other countries are happy and peaceful, while America struggles. There are lots of countries thriving right now, with happiness and peace, while America is struggling with debt, war and many other things. We aren't exactly strong right now, but the world is not suffering either, so it has no connection. Sure, lots of countries are struggling, but that's because they have issues of their own, and it's not a direct result of America's strength or lack of it. I think it depends on the country, its attitude, and sense of community, when determining peace and prosperity.