Problems adding a datacolumn to a datatable

I'm trying to dynamically add datacolumns to a datatable, then reflect those changes in a datagridview. This is what I have to add them:

Code:

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Private Sub BindingNavigatorAddNewItem_Click(sender As System.Object, e As System.EventArgs) Handles BindingNavigatorAddNewItem.Click
        Dim i As Integer = DataSet1.Tables(0).Columns.Count + 1
        Dim col As New DataColumn
        col.ColumnName = i.ToString

        'Creates a blank row if there are no columns
        If i = 1 Then
            DataSet1.Tables(0).NewRow()
        End If

        'Creates the new column
        DataSet1.Tables(0).Columns.Add(col)

        'Refreshes the datagridview
        DataGridView1.Refresh()
    End Sub

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This is what I'm using to remove them:

Code:

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Private Sub BindingNavigatorDeleteItem_Click(sender As System.Object, e As System.EventArgs) Handles BindingNavigatorDeleteItem.Click
        'Iterates through each selected column
        For Each col As DataGridViewColumn In DataGridView1.SelectedColumns
            'Removes those columns
            DataSet1.Tables(0).Columns.Remove(col.Name)
        Next

        'If there are no columns left then delete all the rows
        If DataSet1.Tables(0).Columns.Count = 0 Then
            For Each dr As DataRow In DataGridView1.Rows
                DataSet1.Tables(0).Rows.Remove(dr)
            Next
        End If

        'Refreshes the datagridview
        DataGridView1.Refresh()
    End Sub

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When I click my add button, the countitem goes up and when I click my delete button the countitme goes down. My problem is that the changes aren't reflecting in the datagridview. The dataset is untyped. The bindingsource and the datagridview's datasource is dataset1 and the datamember is table1. Any suggestions?

Shouldnt "DataSet1.Tables(0)"
be
"DataSet1.Tables(1)
or
DataSet1.Tables("Tables1")

?

The following loads a DataTable into a BindingSource, the BindingSource.DataSource is assigned the DataTable

Code:

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Public Class Form1
    WithEvents bsData As New BindingSource

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Code:

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bsData.DataSource = LoadMockedServiceItems()

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The DataGridView DataSource is the BindingSource

Code:

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DataGridView1.DataSource = bsData

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Pressing a Button either adds or removes a specific column from the DataTable as per above. When this happens the DataGridView reflects the add or removal of the column NewColumn1.

Code:

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Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
    Dim dt As DataTable = DirectCast(bsData.DataSource, DataTable)
    If dt.Columns.Contains("NewColumn1") Then
        dt.Columns.Remove("NewColumn1")
    Else
        dt.Columns.Add(New DataColumn With {.ColumnName = "NewColumn1"})
    End If
End Sub

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Quote:

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Shouldnt "DataSet1.Tables(0)"
be
"DataSet1.Tables(1)

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Nope, it could be Table1 because that's the name of it. However, an index out of range would get thrown if I change it to 1.

@Kevin,
Thank you for the detailed reply. I get it now :]