Is it true that you should not look at the sun even during a total solar eclipse?

There is a misunderstanding being circulated that during a total solar eclipse when the moon has fully blocked the light from the sun, that there are still harmful ‘rays’ that can injure your eyes.  This is completely false. When the bright photosphere of the sun is completely covered, only the faint light from the corona is visible, and this radiation is too weak to have any harmful effects on the human retina.  
The misunderstanding comes about because of using the general term ‘solar eclipse’ to describe both the total phase when the sun disk is completely blocked, and the minutes before and after totality when there is still some of the sun’s disk visible. It is harmful to view even a sliver of the sun disk because of its intensity, and so to simply say that you should not view a solar eclipse is rather inaccurate.